The peculiar notion of exchange forces - I: Origins in quantum mechanics, 1926-1928

Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics

Volumn 27, Issue 1, 1996, Pages 23-45

  Carson, Cathryn ^a  

^a STANFORD UNIVERSITY   (United States)

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[No Author keywords available]

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EID: 0030097797     PISSN: 13552198     EISSN: 18792502     Source Type: Journal    
DOI: 10.1016/1355-2198(95)00021-6     Document Type: Article

References (110)

1. 1 Daniel N. Lapedes (ed.), McGraw-Hill Dictionary of Physics and Mathematics (New York: McGraw-Hill, 1978).
2. 2 W. Heitler and F. London, 'Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik', Zeitschrift für Physik 44 (1927), 455-472. See also David A. Bantz, 'The Structure of Discovery: Evolution of Structural Accounts of Chemical Bonding', in Thomas Nickels (ed.), Scientific Discovery: Case Studies (Dordrecht: D. Reidel, 1980), pp. 291-329; Kostas Gavroglu and Ana Simòes, 'The Americans, the Germans, and the Beginnings of Quantum Chemistry', Historical Studies in the Physical and Biological Sciences 25 (1994), 47-110.
3. 2 W. Heitler and F. London, 'Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik', Zeitschrift für Physik 44 (1927), 455-472. See also David A. Bantz, 'The Structure of Discovery: Evolution of Structural Accounts of Chemical Bonding', in Thomas Nickels (ed.), Scientific Discovery: Case Studies (Dordrecht: D. Reidel, 1980), pp. 291-329; Kostas Gavroglu and Ana Simòes, 'The Americans, the Germans, and the Beginnings of Quantum Chemistry', Historical Studies in the Physical and Biological Sciences 25 (1994), 47-110.
4. 2 W. Heitler and F. London, 'Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik', Zeitschrift für Physik 44 (1927), 455-472. See also David A. Bantz, 'The Structure of Discovery: Evolution of Structural Accounts of Chemical Bonding', in Thomas Nickels (ed.), Scientific Discovery: Case Studies (Dordrecht: D. Reidel, 1980), pp. 291-329; Kostas Gavroglu and Ana Simòes, 'The Americans, the Germans, and the Beginnings of Quantum Chemistry', Historical Studies in the Physical and Biological Sciences 25 (1994), 47-110.
5. 3 Only spatial wave functions are under consideration here, and normalization factors are omitted.
6. 4 Heitler and London, op. cit., Note 2, p. 461.
7. 5 The language of 'exchange forces' was connected with the chemists' talk of 'valence forces'; see, e.g. W. Heitler, 'Der gegenwärtige Stand der quantenmechanischen Theorie der homöopolaren Bindung', Physikalische Zeitschrift 31 (1930), 185-204; F. Hund, 'Zur Frage der chemischen Bindung', Zeitschrift für Physik 73 (1931), 1-30.
8. 5 The language of 'exchange forces' was connected with the chemists' talk of 'valence forces'; see, e.g. W. Heitler, 'Der gegenwärtige Stand der quantenmechanischen Theorie der homöopolaren Bindung', Physikalische Zeitschrift 31 (1930), 185-204; F. Hund, 'Zur Frage der chemischen Bindung', Zeitschrift für Physik 73 (1931), 1-30.
9. 6 C.W.F. Everitt and W.M. Fairbank, 'London, Fritz', in Charles Coulston Gillispie (ed.), Dictionary of Scientific Biography (New York: Scribner, 1973).
10. 7 Heitler and London, op. cit., note 2, p. 460, footnote 1. Note that they worked out this picture before dealing with the spins of the electrons, which are oppositely oriented in the ground state.
11. 8 W. Heitler, 'Störungsenergie und Austausch beim Mehrkörperprobleme', Zeitschrift für Physik 46 (1927), 47-72; W. Heitler, 'Elektronenaustausch und Molekülbildung', Gesellschaft der Wissenschaften zu Göttingen, Nachrichten (1927), 368-374. London is also known for his contributions to transformation theory, measurement theory, and superconductivity and superfluidity; his original training was in philosophy.
12. 8 W. Heitler, 'Störungsenergie und Austausch beim Mehrkörperprobleme', Zeitschrift für Physik 46 (1927), 47-72; W. Heitler, 'Elektronenaustausch und Molekülbildung', Gesellschaft der Wissenschaften zu Göttingen, Nachrichten (1927), 368-374. London is also known for his contributions to transformation theory, measurement theory, and superconductivity and superfluidity; his original training was in philosophy.
13. 9 Thanks to careful work we are coming to a more detailed understanding of the evolution of the interpretive debate. See Mara Beller, 'The Birth of Bohr's Complementarity: The Context and the Dialogues', Studies in History and Philosophy of Science 23 (1992), 147-180; Mara Beller, 'Born's Probabilistic Interpretation: A Case Study of "Concepts in Flux"', Studies in History and Philosophy of Science 21 (1990), 563-588; Nancy Cartwright, 'Max Born and the Reality of Quantum Probabilities', in Lorenz Krüger, Gerd Gigerenzer, and Mary S. Morgan (eds), The Probabilistic Revolution, Vol. 2, Ideas in the Sciences (Cambridge, MA: MIT Press, 1988), pp. 409-16; John Hendry, The Creation of Quantum Mechanics and the Bohr-Pauli Dialogue (Dordrecht: D. Reidel, 1984); Mara Beller, 'Matrix Theory before Schrödinger: Philosophy, Problems, Consequences', Isis 74 (1983), 469-491; Edward M. MacKinnon, Scientific Explanation and Atomic Physics (Chicago: University of Chicago Press, 1982); Linda Wessels, 'What was Born's Statistical Interpretation?', in Peter D. Asquith and Ronald N. Giere (eds), PSA 1980 (East Lansing, MI: Philosophy of Science Association, 1981), Vol. 2, pp. 187-200; Linda Wessels, 'The Intellectual Sources of Schrödinger's Interpretations', in Patrick Suppes (ed.). Studies in the Foundations of Quantum Mechanics (East Lansing, MI: Philosophy of Science Association, 1980), pp. 59-76; Edward M. MacKinnon, 'The Rise and Fall of the Schrödinger Interpretation', ibid., pp. 1-57; as well as Olivier Darrigol, From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory (Berkeley: University of California Press, 1992), and Max Jammer, The Conceptual Development of Quantum Mechanics (New York: McGraw-Hill, 1966).
14. 9 Thanks to careful work we are coming to a more detailed understanding of the evolution of the interpretive debate. See Mara Beller, 'The Birth of Bohr's Complementarity: The Context and the Dialogues', Studies in History and Philosophy of Science 23 (1992), 147-180; Mara Beller, 'Born's Probabilistic Interpretation: A Case Study of "Concepts in Flux"', Studies in History and Philosophy of Science 21 (1990), 563-588; Nancy Cartwright, 'Max Born and the Reality of Quantum Probabilities', in Lorenz Krüger, Gerd Gigerenzer, and Mary S. Morgan (eds), The Probabilistic Revolution, Vol. 2, Ideas in the Sciences (Cambridge, MA: MIT Press, 1988), pp. 409-16; John Hendry, The Creation of Quantum Mechanics and the Bohr-Pauli Dialogue (Dordrecht: D. Reidel, 1984); Mara Beller, 'Matrix Theory before Schrödinger: Philosophy, Problems, Consequences', Isis 74 (1983), 469-491; Edward M. MacKinnon, Scientific Explanation and Atomic Physics (Chicago: University of Chicago Press, 1982); Linda Wessels, 'What was Born's Statistical Interpretation?', in Peter D. Asquith and Ronald N. Giere (eds), PSA 1980 (East Lansing, MI: Philosophy of Science Association, 1981), Vol. 2, pp. 187-200; Linda Wessels, 'The Intellectual Sources of Schrödinger's Interpretations', in Patrick Suppes (ed.). Studies in the Foundations of Quantum Mechanics (East Lansing, MI: Philosophy of Science Association, 1980), pp. 59-76; Edward M. MacKinnon, 'The Rise and Fall of the Schrödinger Interpretation', ibid., pp. 1-57; as well as Olivier Darrigol, From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory (Berkeley: University of California Press, 1992), and Max Jammer, The Conceptual Development of Quantum Mechanics (New York: McGraw-Hill, 1966).
15. 9 Thanks to careful work we are coming to a more detailed understanding of the evolution of the interpretive debate. See Mara Beller, 'The Birth of Bohr's Complementarity: The Context and the Dialogues', Studies in History and Philosophy of Science 23 (1992), 147-180; Mara Beller, 'Born's Probabilistic Interpretation: A Case Study of "Concepts in Flux"', Studies in History and Philosophy of Science 21 (1990), 563-588; Nancy Cartwright, 'Max Born and the Reality of Quantum Probabilities', in Lorenz Krüger, Gerd Gigerenzer, and Mary S. Morgan (eds), The Probabilistic Revolution, Vol. 2, Ideas in the Sciences (Cambridge, MA: MIT Press, 1988), pp. 409-16; John Hendry, The Creation of Quantum Mechanics and the Bohr-Pauli Dialogue (Dordrecht: D. Reidel, 1984); Mara Beller, 'Matrix Theory before Schrödinger: Philosophy, Problems, Consequences', Isis 74 (1983), 469-491; Edward M. MacKinnon, Scientific Explanation and Atomic Physics (Chicago: University of Chicago Press, 1982); Linda Wessels, 'What was Born's Statistical Interpretation?', in Peter D. Asquith and Ronald N. Giere (eds), PSA 1980 (East Lansing, MI: Philosophy of Science Association, 1981), Vol. 2, pp. 187-200; Linda Wessels, 'The Intellectual Sources of Schrödinger's Interpretations', in Patrick Suppes (ed.). Studies in the Foundations of Quantum Mechanics (East Lansing, MI: Philosophy of Science Association, 1980), pp. 59-76; Edward M. MacKinnon, 'The Rise and Fall of the Schrödinger Interpretation', ibid., pp. 1-57; as well as Olivier Darrigol, From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory (Berkeley: University of California Press, 1992), and Max Jammer, The Conceptual Development of Quantum Mechanics (New York: McGraw-Hill, 1966).
16. 9 Thanks to careful work we are coming to a more detailed understanding of the evolution of the interpretive debate. See Mara Beller, 'The Birth of Bohr's Complementarity: The Context and the Dialogues', Studies in History and Philosophy of Science 23 (1992), 147-180; Mara Beller, 'Born's Probabilistic Interpretation: A Case Study of "Concepts in Flux"', Studies in History and Philosophy of Science 21 (1990), 563-588; Nancy Cartwright, 'Max Born and the Reality of Quantum Probabilities', in Lorenz Krüger, Gerd Gigerenzer, and Mary S. Morgan (eds), The Probabilistic Revolution, Vol. 2, Ideas in the Sciences (Cambridge, MA: MIT Press, 1988), pp. 409-16; John Hendry, The Creation of Quantum Mechanics and the Bohr-Pauli Dialogue (Dordrecht: D. Reidel, 1984); Mara Beller, 'Matrix Theory before Schrödinger: Philosophy, Problems, Consequences', Isis 74 (1983), 469-491; Edward M. MacKinnon, Scientific Explanation and Atomic Physics (Chicago: University of Chicago Press, 1982); Linda Wessels, 'What was Born's Statistical Interpretation?', in Peter D. Asquith and Ronald N. Giere (eds), PSA 1980 (East Lansing, MI: Philosophy of Science Association, 1981), Vol. 2, pp. 187-200; Linda Wessels, 'The Intellectual Sources of Schrödinger's Interpretations', in Patrick Suppes (ed.). Studies in the Foundations of Quantum Mechanics (East Lansing, MI: Philosophy of Science Association, 1980), pp. 59-76; Edward M. MacKinnon, 'The Rise and Fall of the Schrödinger Interpretation', ibid., pp. 1-57; as well as Olivier Darrigol, From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory (Berkeley: University of California Press, 1992), and Max Jammer, The Conceptual Development of Quantum Mechanics (New York: McGraw-Hill, 1966).
17. 9 Thanks to careful work we are coming to a more detailed understanding of the evolution of the interpretive debate. See Mara Beller, 'The Birth of Bohr's Complementarity: The Context and the Dialogues', Studies in History and Philosophy of Science 23 (1992), 147-180; Mara Beller, 'Born's Probabilistic Interpretation: A Case Study of "Concepts in Flux"', Studies in History and Philosophy of Science 21 (1990), 563-588; Nancy Cartwright, 'Max Born and the Reality of Quantum Probabilities', in Lorenz Krüger, Gerd Gigerenzer, and Mary S. Morgan (eds), The Probabilistic Revolution, Vol. 2, Ideas in the Sciences (Cambridge, MA: MIT Press, 1988), pp. 409-16; John Hendry, The Creation of Quantum Mechanics and the Bohr-Pauli Dialogue (Dordrecht: D. Reidel, 1984); Mara Beller, 'Matrix Theory before Schrödinger: Philosophy, Problems, Consequences', Isis 74 (1983), 469-491; Edward M. MacKinnon, Scientific Explanation and Atomic Physics (Chicago: University of Chicago Press, 1982); Linda Wessels, 'What was Born's Statistical Interpretation?', in Peter D. Asquith and Ronald N. Giere (eds), PSA 1980 (East Lansing, MI: Philosophy of Science Association, 1981), Vol. 2, pp. 187-200; Linda Wessels, 'The Intellectual Sources of Schrödinger's Interpretations', in Patrick Suppes (ed.). Studies in the Foundations of Quantum Mechanics (East Lansing, MI: Philosophy of Science Association, 1980), pp. 59-76; Edward M. MacKinnon, 'The Rise and Fall of the Schrödinger Interpretation', ibid., pp. 1-57; as well as Olivier Darrigol, From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory (Berkeley: University of California Press, 1992), and Max Jammer, The Conceptual Development of Quantum Mechanics (New York: McGraw-Hill, 1966).
18. 9 Thanks to careful work we are coming to a more detailed understanding of the evolution of the interpretive debate. See Mara Beller, 'The Birth of Bohr's Complementarity: The Context and the Dialogues', Studies in History and Philosophy of Science 23 (1992), 147-180; Mara Beller, 'Born's Probabilistic Interpretation: A Case Study of "Concepts in Flux"', Studies in History and Philosophy of Science 21 (1990), 563-588; Nancy Cartwright, 'Max Born and the Reality of Quantum Probabilities', in Lorenz Krüger, Gerd Gigerenzer, and Mary S. Morgan (eds), The Probabilistic Revolution, Vol. 2, Ideas in the Sciences (Cambridge, MA: MIT Press, 1988), pp. 409-16; John Hendry, The Creation of Quantum Mechanics and the Bohr-Pauli Dialogue (Dordrecht: D. Reidel, 1984); Mara Beller, 'Matrix Theory before Schrödinger: Philosophy, Problems, Consequences', Isis 74 (1983), 469-491; Edward M. MacKinnon, Scientific Explanation and Atomic Physics (Chicago: University of Chicago Press, 1982); Linda Wessels, 'What was Born's Statistical Interpretation?', in Peter D. Asquith and Ronald N. Giere (eds), PSA 1980 (East Lansing, MI: Philosophy of Science Association, 1981), Vol. 2, pp. 187-200; Linda Wessels, 'The Intellectual Sources of Schrödinger's Interpretations', in Patrick Suppes (ed.). Studies in the Foundations of Quantum Mechanics (East Lansing, MI: Philosophy of Science Association, 1980), pp. 59-76; Edward M. MacKinnon, 'The Rise and Fall of the Schrödinger Interpretation', ibid., pp. 1-57; as well as Olivier Darrigol, From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory (Berkeley: University of California Press, 1992), and Max Jammer, The Conceptual Development of Quantum Mechanics (New York: McGraw-Hill, 1966).
19. 9 Thanks to careful work we are coming to a more detailed understanding of the evolution of the interpretive debate. See Mara Beller, 'The Birth of Bohr's Complementarity: The Context and the Dialogues', Studies in History and Philosophy of Science 23 (1992), 147-180; Mara Beller, 'Born's Probabilistic Interpretation: A Case Study of "Concepts in Flux"', Studies in History and Philosophy of Science 21 (1990), 563-588; Nancy Cartwright, 'Max Born and the Reality of Quantum Probabilities', in Lorenz Krüger, Gerd Gigerenzer, and Mary S. Morgan (eds), The Probabilistic Revolution, Vol. 2, Ideas in the Sciences (Cambridge, MA: MIT Press, 1988), pp. 409-16; John Hendry, The Creation of Quantum Mechanics and the Bohr-Pauli Dialogue (Dordrecht: D. Reidel, 1984); Mara Beller, 'Matrix Theory before Schrödinger: Philosophy, Problems, Consequences', Isis 74 (1983), 469-491; Edward M. MacKinnon, Scientific Explanation and Atomic Physics (Chicago: University of Chicago Press, 1982); Linda Wessels, 'What was Born's Statistical Interpretation?', in Peter D. Asquith and Ronald N. Giere (eds), PSA 1980 (East Lansing, MI: Philosophy of Science Association, 1981), Vol. 2, pp. 187-200; Linda Wessels, 'The Intellectual Sources of Schrödinger's Interpretations', in Patrick Suppes (ed.). Studies in the Foundations of Quantum Mechanics (East Lansing, MI: Philosophy of Science Association, 1980), pp. 59-76; Edward M. MacKinnon, 'The Rise and Fall of the Schrödinger Interpretation', ibid., pp. 1-57; as well as Olivier Darrigol, From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory (Berkeley: University of California Press, 1992), and Max Jammer, The Conceptual Development of Quantum Mechanics (New York: McGraw-Hill, 1966).
20. 9 Thanks to careful work we are coming to a more detailed understanding of the evolution of the interpretive debate. See Mara Beller, 'The Birth of Bohr's Complementarity: The Context and the Dialogues', Studies in History and Philosophy of Science 23 (1992), 147-180; Mara Beller, 'Born's Probabilistic Interpretation: A Case Study of "Concepts in Flux"', Studies in History and Philosophy of Science 21 (1990), 563-588; Nancy Cartwright, 'Max Born and the Reality of Quantum Probabilities', in Lorenz Krüger, Gerd Gigerenzer, and Mary S. Morgan (eds), The Probabilistic Revolution, Vol. 2, Ideas in the Sciences (Cambridge, MA: MIT Press, 1988), pp. 409-16; John Hendry, The Creation of Quantum Mechanics and the Bohr-Pauli Dialogue (Dordrecht: D. Reidel, 1984); Mara Beller, 'Matrix Theory before Schrödinger: Philosophy, Problems, Consequences', Isis 74 (1983), 469-491; Edward M. MacKinnon, Scientific Explanation and Atomic Physics (Chicago: University of Chicago Press, 1982); Linda Wessels, 'What was Born's Statistical Interpretation?', in Peter D. Asquith and Ronald N. Giere (eds), PSA 1980 (East Lansing, MI: Philosophy of Science Association, 1981), Vol. 2, pp. 187-200; Linda Wessels, 'The Intellectual Sources of Schrödinger's Interpretations', in Patrick Suppes (ed.). Studies in the Foundations of Quantum Mechanics (East Lansing, MI: Philosophy of Science Association, 1980), pp. 59-76; Edward M. MacKinnon, 'The Rise and Fall of the Schrödinger Interpretation', ibid., pp. 1-57; as well as Olivier Darrigol, From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory (Berkeley: University of California Press, 1992), and Max Jammer, The Conceptual Development of Quantum Mechanics (New York: McGraw-Hill, 1966).
21. 9 Thanks to careful work we are coming to a more detailed understanding of the evolution of the interpretive debate. See Mara Beller, 'The Birth of Bohr's Complementarity: The Context and the Dialogues', Studies in History and Philosophy of Science 23 (1992), 147-180; Mara Beller, 'Born's Probabilistic Interpretation: A Case Study of "Concepts in Flux"', Studies in History and Philosophy of Science 21 (1990), 563-588; Nancy Cartwright, 'Max Born and the Reality of Quantum Probabilities', in Lorenz Krüger, Gerd Gigerenzer, and Mary S. Morgan (eds), The Probabilistic Revolution, Vol. 2, Ideas in the Sciences (Cambridge, MA: MIT Press, 1988), pp. 409-16; John Hendry, The Creation of Quantum Mechanics and the Bohr-Pauli Dialogue (Dordrecht: D. Reidel, 1984); Mara Beller, 'Matrix Theory before Schrödinger: Philosophy, Problems, Consequences', Isis 74 (1983), 469-491; Edward M. MacKinnon, Scientific Explanation and Atomic Physics (Chicago: University of Chicago Press, 1982); Linda Wessels, 'What was Born's Statistical Interpretation?', in Peter D. Asquith and Ronald N. Giere (eds), PSA 1980 (East Lansing, MI: Philosophy of Science Association, 1981), Vol. 2, pp. 187-200; Linda Wessels, 'The Intellectual Sources of Schrödinger's Interpretations', in Patrick Suppes (ed.). Studies in the Foundations of Quantum Mechanics (East Lansing, MI: Philosophy of Science Association, 1980), pp. 59-76; Edward M. MacKinnon, 'The Rise and Fall of the Schrödinger Interpretation', ibid., pp. 1-57; as well as Olivier Darrigol, From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory (Berkeley: University of California Press, 1992), and Max Jammer, The Conceptual Development of Quantum Mechanics (New York: McGraw-Hill, 1966).
22. 9 Thanks to careful work we are coming to a more detailed understanding of the evolution of the interpretive debate. See Mara Beller, 'The Birth of Bohr's Complementarity: The Context and the Dialogues', Studies in History and Philosophy of Science 23 (1992), 147-180; Mara Beller, 'Born's Probabilistic Interpretation: A Case Study of "Concepts in Flux"', Studies in History and Philosophy of Science 21 (1990), 563-588; Nancy Cartwright, 'Max Born and the Reality of Quantum Probabilities', in Lorenz Krüger, Gerd Gigerenzer, and Mary S. Morgan (eds), The Probabilistic Revolution, Vol. 2, Ideas in the Sciences (Cambridge, MA: MIT Press, 1988), pp. 409-16; John Hendry, The Creation of Quantum Mechanics and the Bohr-Pauli Dialogue (Dordrecht: D. Reidel, 1984); Mara Beller, 'Matrix Theory before Schrödinger: Philosophy, Problems, Consequences', Isis 74 (1983), 469-491; Edward M. MacKinnon, Scientific Explanation and Atomic Physics (Chicago: University of Chicago Press, 1982); Linda Wessels, 'What was Born's Statistical Interpretation?', in Peter D. Asquith and Ronald N. Giere (eds), PSA 1980 (East Lansing, MI: Philosophy of Science Association, 1981), Vol. 2, pp. 187-200; Linda Wessels, 'The Intellectual Sources of Schrödinger's Interpretations', in Patrick Suppes (ed.). Studies in the Foundations of Quantum Mechanics (East Lansing, MI: Philosophy of Science Association, 1980), pp. 59-76; Edward M. MacKinnon, 'The Rise and Fall of the Schrödinger Interpretation', ibid., pp. 1-57; as well as Olivier Darrigol, From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory (Berkeley: University of California Press, 1992), and Max Jammer, The Conceptual Development of Quantum Mechanics (New York: McGraw-Hill, 1966).
23. 9 Thanks to careful work we are coming to a more detailed understanding of the evolution of the interpretive debate. See Mara Beller, 'The Birth of Bohr's Complementarity: The Context and the Dialogues', Studies in History and Philosophy of Science 23 (1992), 147-180; Mara Beller, 'Born's Probabilistic Interpretation: A Case Study of "Concepts in Flux"', Studies in History and Philosophy of Science 21 (1990), 563-588; Nancy Cartwright, 'Max Born and the Reality of Quantum Probabilities', in Lorenz Krüger, Gerd Gigerenzer, and Mary S. Morgan (eds), The Probabilistic Revolution, Vol. 2, Ideas in the Sciences (Cambridge, MA: MIT Press, 1988), pp. 409-16; John Hendry, The Creation of Quantum Mechanics and the Bohr-Pauli Dialogue (Dordrecht: D. Reidel, 1984); Mara Beller, 'Matrix Theory before Schrödinger: Philosophy, Problems, Consequences', Isis 74 (1983), 469-491; Edward M. MacKinnon, Scientific Explanation and Atomic Physics (Chicago: University of Chicago Press, 1982); Linda Wessels, 'What was Born's Statistical Interpretation?', in Peter D. Asquith and Ronald N. Giere (eds), PSA 1980 (East Lansing, MI: Philosophy of Science Association, 1981), Vol. 2, pp. 187-200; Linda Wessels, 'The Intellectual Sources of Schrödinger's Interpretations', in Patrick Suppes (ed.). Studies in the Foundations of Quantum Mechanics (East Lansing, MI: Philosophy of Science Association, 1980), pp. 59-76; Edward M. MacKinnon, 'The Rise and Fall of the Schrödinger Interpretation', ibid., pp. 1-57; as well as Olivier Darrigol, From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory (Berkeley: University of California Press, 1992), and Max Jammer, The Conceptual Development of Quantum Mechanics (New York: McGraw-Hill, 1966).
24. 10 E. Schrödinger, 'Quantisierung als Eigenwertproblem (Vierte Mitteilung)', Annalen der Physik 81 (1926), 109-139, see p. 135; Schrödinger to Lorentz, 6 June 1926, in K. Przibram (ed.), Briefe zur Wellenmechanik (Wien: Springer, 1963), p. 51.
25. 10 E. Schrödinger, 'Quantisierung als Eigenwertproblem (Vierte Mitteilung)', Annalen der Physik 81 (1926), 109-139, see p. 135; Schrödinger to Lorentz, 6 June 1926, in K. Przibram (ed.), Briefe zur Wellenmechanik (Wien: Springer, 1963), p. 51.
26. 11 W. Heisenberg, 'Mehrkörperproblem und Resonanz in der Quantenmechanik', Zeitschrift für Physik 38 (1926), 411-126.
27. 12 For the background to Heisenberg's work on the helium problem see Jagdish Mehra and Helmut Rechenberg, The Historical Development of Quantum Theory, Vol. 3, The Formulation of Matrix Mechanics and its Modifications, 1925-1926 (New York: Springer, 1982), pp. 285-289.
28. 13 See, however, W. Kossel, 'Über gekoppelte Oszillatoren', Physikalische Zeitschrift 32 (1931), 172-179.
29. 14 Op. cit., note 11, p. 417. Many of Heisenberg's results were also obtained in P.A.M. Dirac, 'On the Theory of Quantum Mechanics', Royal Society of London, Proceedings A112 (1926), 661-677; what Heisenberg described with the expressions 'Plätze tauschen' or 'Vertauschung' Dirac called 'interchange'. Dirac's work was, however, less influential for the development that followed.
30. 14 Op. cit., note 11, p. 417. Many of Heisenberg's results were also obtained in P.A.M. Dirac, 'On the Theory of Quantum Mechanics', Royal Society of London, Proceedings A112 (1926), 661-677; what Heisenberg described with the expressions 'Plätze tauschen' or 'Vertauschung' Dirac called 'interchange'. Dirac's work was, however, less influential for the development that followed.
31. 15 The symmetry character of these solutions allowed only certain kinds of transitions between levels, which explained the essential features of the helium spectrum. See also W. Heisenberg, 'Über die Spektra von Atomsystemen mit zwei Elektronen', Zeitschrift für Physik 39 (1926), 499-518; W. Heisenberg, 'Mehrkörperprobleme und Resonanz in der Quantenmechanik, II', Zeitschrift für Physik 41 (1927), 239-267. There is of course much more going on in Heisenberg's paper than I describe in connection with resonance, as is indeed true of all of the papers that will come under discussion.
32. 15 The symmetry character of these solutions allowed only certain kinds of transitions between levels, which explained the essential features of the helium spectrum. See also W. Heisenberg, 'Über die Spektra von Atomsystemen mit zwei Elektronen', Zeitschrift für Physik 39 (1926), 499-518; W. Heisenberg, 'Mehrkörperprobleme und Resonanz in der Quantenmechanik, II', Zeitschrift für Physik 41 (1927), 239-267. There is of course much more going on in Heisenberg's paper than I describe in connection with resonance, as is indeed true of all of the papers that will come under discussion.
33. 16 See also Arthur I. Miller, 'Redefining Visualizability', in Imagery in Scientific Thought: Creating 20th-Century Physics (Boston: Birkhäuser, 1984), pp. 125-183.
34. 17 Op. cit., note 11, p. 421; see also p. 417.
35. 18 Ibid., pp. 417-418.
36. 19 See, for example, Heisenberg's insistence on this point in Heisenberg to Pauli, 28 October 1926, in Wolfgang Pauli, Wissenschaftlicher Briefwechsel, A. Hermann, K. V. Meyenn, and V. F. Weisskopf (eds), Vol. 1, 1919-1929 (New York: Springer, 1979), p. 351.
37. 20 Op. cit., note 11, p. 417; cf. Albrecht Unsöld, 'Beiträge zur Quantenmechanik der Atome', Annalen der Physik 82 (1927), 355-393, see p. 365, where Heisenberg's 'Plätze tauschen' is also called an 'Austausch'.
38. 20 Op. cit., note 11, p. 417; cf. Albrecht Unsöld, 'Beiträge zur Quantenmechanik der Atome', Annalen der Physik 82 (1927), 355-393, see p. 365, where Heisenberg's 'Plätze tauschen' is also called an 'Austausch'.
39. 21 Cf. Beller, 'Born's Probabilistic Interpretation', op. cit., note 9; Cartwright, op. cit, note 9; Wessels, 'Born's Statistical Interpretation', op. cit., note 9.
40. 21 Cf. Beller, 'Born's Probabilistic Interpretation', op. cit., note 9; Cartwright, op. cit, note 9; Wessels, 'Born's Statistical Interpretation', op. cit., note 9.
41. 21 Cf. Beller, 'Born's Probabilistic Interpretation', op. cit., note 9; Cartwright, op. cit, note 9; Wessels, 'Born's Statistical Interpretation', op. cit., note 9.
42. 22 Schrödinger interpreted superpositions of eigenfunctions with different energy eigenvalues in terms of oscillating dipole moments that gave rise to radiation. Superpositions of degenerate states could not be so interpreted.
43. 23 M. Born, 'Das Adiabatenprinzip in der Quantenmechanik', Zeitschrift für Physik 40 (1926), 167-192; cf. M. Born, 'Zur Quantenmechanik der Stoßvorgänge', Zeitschrift für Physik 37 (1926), 863-867; M. Born, 'Quantenmechanik der Stoßvorgänge', Zeitschrift für Physik 38 (1926), 803-827; as well as M. Born and V. Fock, 'Beweis des Adiabatensatzes', Zeitschrift für Physik 51 (1928), 165-180, which discusses issues associated with degeneracy.
44. 23 M. Born, 'Das Adiabatenprinzip in der Quantenmechanik', Zeitschrift für Physik 40 (1926), 167-192; cf. M. Born, 'Zur Quantenmechanik der Stoßvorgänge', Zeitschrift für Physik 37 (1926), 863-867; M. Born, 'Quantenmechanik der Stoßvorgänge', Zeitschrift für Physik 38 (1926), 803-827; as well as M. Born and V. Fock, 'Beweis des Adiabatensatzes', Zeitschrift für Physik 51 (1928), 165-180, which discusses issues associated with degeneracy.
45. 23 M. Born, 'Das Adiabatenprinzip in der Quantenmechanik', Zeitschrift für Physik 40 (1926), 167-192; cf. M. Born, 'Zur Quantenmechanik der Stoßvorgänge', Zeitschrift für Physik 37 (1926), 863-867; M. Born, 'Quantenmechanik der Stoßvorgänge', Zeitschrift für Physik 38 (1926), 803-827; as well as M. Born and V. Fock, 'Beweis des Adiabatensatzes', Zeitschrift für Physik 51 (1928), 165-180, which discusses issues associated with degeneracy.
46. 23 M. Born, 'Das Adiabatenprinzip in der Quantenmechanik', Zeitschrift für Physik 40 (1926), 167-192; cf. M. Born, 'Zur Quantenmechanik der Stoßvorgänge', Zeitschrift für Physik 37 (1926), 863-867; M. Born, 'Quantenmechanik der Stoßvorgänge', Zeitschrift für Physik 38 (1926), 803-827; as well as M. Born and V. Fock, 'Beweis des Adiabatensatzes', Zeitschrift für Physik 51 (1928), 165-180, which discusses issues associated with degeneracy.
47. 24 E.g. P. Jordan, 'Über eine neue Begründung der Quantenmechanik', Zeitschrift für Physik 40 (1927), 809-838, see p. 811.
48. 25 This seems to have held not only for those who took up Born's approach to calculate collisions, including Wentzel, Oppenheimer, and Elsasser, but also for those (other than Jordan) who helped build up a more general statistical interpretation, such as Pauli, Heisenberg, and Dirac. G. Wentzel, 'Zwei Bemerkungen über die Zerstreuung korpuskularer Strahlen als Beugungserscheinung', Zeitschrift für Physik 40 (1926), 590-593; J. R. Oppenheimer, 'Bemerkung zur Zerstreuung der a-Teilchen', Zeitschrift für Physik 43 (1927), 413-415; W. Elsasser, 'Zur Theorie der Stoßprozesse bei Wasserstoff', Zeitschrift für Physik 45 (1927), 522-538; W. Pauli, 'Über Gasentartung und Paramagnetismus', Zeitschrift für Physik 41 (1927), 81-102, see p. 83, footnote 1; W. Heisenberg, 'Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik', Zeitschrift für Physik 43 (1927), 172-198, see p. 176, footnote 1; Dirac, op. cit., note 14; P. Dirac, 'Über die Quantenmechanik der Stoßvorgänge', Zeitschrift für Physik 44 (1927), 585-595; P. A. M. Dirac, 'The Physical Interpretation of the Quantum Dynamics', Royal Society of London, Proceedings A113 (1927), 621-641, see p. 621; P. A. M. Dirac, 'The Quantum Theory of the Emission and Absorption of Radiation', Royal Society of London, Proceedings A114 (1927), 243-265, see pp. 256-260.
49. 25 This seems to have held not only for those who took up Born's approach to calculate collisions, including Wentzel, Oppenheimer, and Elsasser, but also for those (other than Jordan) who helped build up a more general statistical interpretation, such as Pauli, Heisenberg, and Dirac. G. Wentzel, 'Zwei Bemerkungen über die Zerstreuung korpuskularer Strahlen als Beugungserscheinung', Zeitschrift für Physik 40 (1926), 590-593; J. R. Oppenheimer, 'Bemerkung zur Zerstreuung der a-Teilchen', Zeitschrift für Physik 43 (1927), 413-415; W. Elsasser, 'Zur Theorie der Stoßprozesse bei Wasserstoff', Zeitschrift für Physik 45 (1927), 522-538; W. Pauli, 'Über Gasentartung und Paramagnetismus', Zeitschrift für Physik 41 (1927), 81-102, see p. 83, footnote 1; W. Heisenberg, 'Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik', Zeitschrift für Physik 43 (1927), 172-198, see p. 176, footnote 1; Dirac, op. cit., note 14; P. Dirac, 'Über die Quantenmechanik der Stoßvorgänge', Zeitschrift für Physik 44 (1927), 585-595; P. A. M. Dirac, 'The Physical Interpretation of the Quantum Dynamics', Royal Society of London, Proceedings A113 (1927), 621-641, see p. 621; P. A. M. Dirac, 'The Quantum Theory of the Emission and Absorption of Radiation', Royal Society of London, Proceedings A114 (1927), 243-265, see pp. 256-260.
50. 25 This seems to have held not only for those who took up Born's approach to calculate collisions, including Wentzel, Oppenheimer, and Elsasser, but also for those (other than Jordan) who helped build up a more general statistical interpretation, such as Pauli, Heisenberg, and Dirac. G. Wentzel, 'Zwei Bemerkungen über die Zerstreuung korpuskularer Strahlen als Beugungserscheinung', Zeitschrift für Physik 40 (1926), 590-593; J. R. Oppenheimer, 'Bemerkung zur Zerstreuung der a-Teilchen', Zeitschrift für Physik 43 (1927), 413-415; W. Elsasser, 'Zur Theorie der Stoßprozesse bei Wasserstoff', Zeitschrift für Physik 45 (1927), 522-538; W. Pauli, 'Über Gasentartung und Paramagnetismus', Zeitschrift für Physik 41 (1927), 81-102, see p. 83, footnote 1; W. Heisenberg, 'Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik', Zeitschrift für Physik 43 (1927), 172-198, see p. 176, footnote 1; Dirac, op. cit., note 14; P. Dirac, 'Über die Quantenmechanik der Stoßvorgänge', Zeitschrift für Physik 44 (1927), 585-595; P. A. M. Dirac, 'The Physical Interpretation of the Quantum Dynamics', Royal Society of London, Proceedings A113 (1927), 621-641, see p. 621; P. A. M. Dirac, 'The Quantum Theory of the Emission and Absorption of Radiation', Royal Society of London, Proceedings A114 (1927), 243-265, see pp. 256-260.
51. 25 This seems to have held not only for those who took up Born's approach to calculate collisions, including Wentzel, Oppenheimer, and Elsasser, but also for those (other than Jordan) who helped build up a more general statistical interpretation, such as Pauli, Heisenberg, and Dirac. G. Wentzel, 'Zwei Bemerkungen über die Zerstreuung korpuskularer Strahlen als Beugungserscheinung', Zeitschrift für Physik 40 (1926), 590-593; J. R. Oppenheimer, 'Bemerkung zur Zerstreuung der a-Teilchen', Zeitschrift für Physik 43 (1927), 413-415; W. Elsasser, 'Zur Theorie der Stoßprozesse bei Wasserstoff', Zeitschrift für Physik 45 (1927), 522-538; W. Pauli, 'Über Gasentartung und Paramagnetismus', Zeitschrift für Physik 41 (1927), 81-102, see p. 83, footnote 1; W. Heisenberg, 'Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik', Zeitschrift für Physik 43 (1927), 172-198, see p. 176, footnote 1; Dirac, op. cit., note 14; P. Dirac, 'Über die Quantenmechanik der Stoßvorgänge', Zeitschrift für Physik 44 (1927), 585-595; P. A. M. Dirac, 'The Physical Interpretation of the Quantum Dynamics', Royal Society of London, Proceedings A113 (1927), 621-641, see p. 621; P. A. M. Dirac, 'The Quantum Theory of the Emission and Absorption of Radiation', Royal Society of London, Proceedings A114 (1927), 243-265, see pp. 256-260.
52. 25 This seems to have held not only for those who took up Born's approach to calculate collisions, including Wentzel, Oppenheimer, and Elsasser, but also for those (other than Jordan) who helped build up a more general statistical interpretation, such as Pauli, Heisenberg, and Dirac. G. Wentzel, 'Zwei Bemerkungen über die Zerstreuung korpuskularer Strahlen als Beugungserscheinung', Zeitschrift für Physik 40 (1926), 590-593; J. R. Oppenheimer, 'Bemerkung zur Zerstreuung der a-Teilchen', Zeitschrift für Physik 43 (1927), 413-415; W. Elsasser, 'Zur Theorie der Stoßprozesse bei Wasserstoff', Zeitschrift für Physik 45 (1927), 522-538; W. Pauli, 'Über Gasentartung und Paramagnetismus', Zeitschrift für Physik 41 (1927), 81-102, see p. 83, footnote 1; W. Heisenberg, 'Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik', Zeitschrift für Physik 43 (1927), 172-198, see p. 176, footnote 1; Dirac, op. cit., note 14; P. Dirac, 'Über die Quantenmechanik der Stoßvorgänge', Zeitschrift für Physik 44 (1927), 585-595; P. A. M. Dirac, 'The Physical Interpretation of the Quantum Dynamics', Royal Society of London, Proceedings A113 (1927), 621-641, see p. 621; P. A. M. Dirac, 'The Quantum Theory of the Emission and Absorption of Radiation', Royal Society of London, Proceedings A114 (1927), 243-265, see pp. 256-260.
53. 25 This seems to have held not only for those who took up Born's approach to calculate collisions, including Wentzel, Oppenheimer, and Elsasser, but also for those (other than Jordan) who helped build up a more general statistical interpretation, such as Pauli, Heisenberg, and Dirac. G. Wentzel, 'Zwei Bemerkungen über die Zerstreuung korpuskularer Strahlen als Beugungserscheinung', Zeitschrift für Physik 40 (1926), 590-593; J. R. Oppenheimer, 'Bemerkung zur Zerstreuung der a-Teilchen', Zeitschrift für Physik 43 (1927), 413-415; W. Elsasser, 'Zur Theorie der Stoßprozesse bei Wasserstoff', Zeitschrift für Physik 45 (1927), 522-538; W. Pauli, 'Über Gasentartung und Paramagnetismus', Zeitschrift für Physik 41 (1927), 81-102, see p. 83, footnote 1; W. Heisenberg, 'Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik', Zeitschrift für Physik 43 (1927), 172-198, see p. 176, footnote 1; Dirac, op. cit., note 14; P. Dirac, 'Über die Quantenmechanik der Stoßvorgänge', Zeitschrift für Physik 44 (1927), 585-595; P. A. M. Dirac, 'The Physical Interpretation of the Quantum Dynamics', Royal Society of London, Proceedings A113 (1927), 621-641, see p. 621; P. A. M. Dirac, 'The Quantum Theory of the Emission and Absorption of Radiation', Royal Society of London, Proceedings A114 (1927), 243-265, see pp. 256-260.
54. 25 This seems to have held not only for those who took up Born's approach to calculate collisions, including Wentzel, Oppenheimer, and Elsasser, but also for those (other than Jordan) who helped build up a more general statistical interpretation, such as Pauli, Heisenberg, and Dirac. G. Wentzel, 'Zwei Bemerkungen über die Zerstreuung korpuskularer Strahlen als Beugungserscheinung', Zeitschrift für Physik 40 (1926), 590-593; J. R. Oppenheimer, 'Bemerkung zur Zerstreuung der a-Teilchen', Zeitschrift für Physik 43 (1927), 413-415; W. Elsasser, 'Zur Theorie der Stoßprozesse bei Wasserstoff', Zeitschrift für Physik 45 (1927), 522-538; W. Pauli, 'Über Gasentartung und Paramagnetismus', Zeitschrift für Physik 41 (1927), 81-102, see p. 83, footnote 1; W. Heisenberg, 'Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik', Zeitschrift für Physik 43 (1927), 172-198, see p. 176, footnote 1; Dirac, op. cit., note 14; P. Dirac, 'Über die Quantenmechanik der Stoßvorgänge', Zeitschrift für Physik 44 (1927), 585-595; P. A. M. Dirac, 'The Physical Interpretation of the Quantum Dynamics', Royal Society of London, Proceedings A113 (1927), 621-641, see p. 621; P. A. M. Dirac, 'The Quantum Theory of the Emission and Absorption of Radiation', Royal Society of London, Proceedings A114 (1927), 243-265, see pp. 256-260.
55. 25 This seems to have held not only for those who took up Born's approach to calculate collisions, including Wentzel, Oppenheimer, and Elsasser, but also for those (other than Jordan) who helped build up a more general statistical interpretation, such as Pauli, Heisenberg, and Dirac. G. Wentzel, 'Zwei Bemerkungen über die Zerstreuung korpuskularer Strahlen als Beugungserscheinung', Zeitschrift für Physik 40 (1926), 590-593; J. R. Oppenheimer, 'Bemerkung zur Zerstreuung der a-Teilchen', Zeitschrift für Physik 43 (1927), 413-415; W. Elsasser, 'Zur Theorie der Stoßprozesse bei Wasserstoff', Zeitschrift für Physik 45 (1927), 522-538; W. Pauli, 'Über Gasentartung und Paramagnetismus', Zeitschrift für Physik 41 (1927), 81-102, see p. 83, footnote 1; W. Heisenberg, 'Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik', Zeitschrift für Physik 43 (1927), 172-198, see p. 176, footnote 1; Dirac, op. cit., note 14; P. Dirac, 'Über die Quantenmechanik der Stoßvorgänge', Zeitschrift für Physik 44 (1927), 585-595; P. A. M. Dirac, 'The Physical Interpretation of the Quantum Dynamics', Royal Society of London, Proceedings A113 (1927), 621-641, see p. 621; P. A. M. Dirac, 'The Quantum Theory of the Emission and Absorption of Radiation', Royal Society of London, Proceedings A114 (1927), 243-265, see pp. 256-260.
56. 25 This seems to have held not only for those who took up Born's approach to calculate collisions, including Wentzel, Oppenheimer, and Elsasser, but also for those (other than Jordan) who helped build up a more general statistical interpretation, such as Pauli, Heisenberg, and Dirac. G. Wentzel, 'Zwei Bemerkungen über die Zerstreuung korpuskularer Strahlen als Beugungserscheinung', Zeitschrift für Physik 40 (1926), 590-593; J. R. Oppenheimer, 'Bemerkung zur Zerstreuung der a-Teilchen', Zeitschrift für Physik 43 (1927), 413-415; W. Elsasser, 'Zur Theorie der Stoßprozesse bei Wasserstoff', Zeitschrift für Physik 45 (1927), 522-538; W. Pauli, 'Über Gasentartung und Paramagnetismus', Zeitschrift für Physik 41 (1927), 81-102, see p. 83, footnote 1; W. Heisenberg, 'Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik', Zeitschrift für Physik 43 (1927), 172-198, see p. 176, footnote 1; Dirac, op. cit., note 14; P. Dirac, 'Über die Quantenmechanik der Stoßvorgänge', Zeitschrift für Physik 44 (1927), 585-595; P. A. M. Dirac, 'The Physical Interpretation of the Quantum Dynamics', Royal Society of London, Proceedings A113 (1927), 621-641, see p. 621; P. A. M. Dirac, 'The Quantum Theory of the Emission and Absorption of Radiation', Royal Society of London, Proceedings A114 (1927), 243-265, see pp. 256-260.
57. 26 For testimony to this effect see, e.g. E. H. Kennard, 'Zur Quantenmechanik einfacher Bewegungstypen', Zeitschrift für Physik 44 (1927), 326-352; F. London, 'Quantentheorie und chemische Bindung', in H. Falkenhagen (ed.), Quantentheorie und Chemie, Leipziger Vorträge 1928 (Leipzig: S. Hirzel, 1928), pp. 59-84, see pp. 61-62, footnote 2; and, in an example to be discussed later at length, F. Hund, 'Zur Deutung der Molekelspektren, III', Zeitschrift für Physik 43 (1927), 805-826, see p. 809, especially footnote 1.
58. 26 For testimony to this effect see, e.g. E. H. Kennard, 'Zur Quantenmechanik einfacher Bewegungstypen', Zeitschrift für Physik 44 (1927), 326-352; F. London, 'Quantentheorie und chemische Bindung', in H. Falkenhagen (ed.), Quantentheorie und Chemie, Leipziger Vorträge 1928 (Leipzig: S. Hirzel, 1928), pp. 59-84, see pp. 61-62, footnote 2; and, in an example to be discussed later at length, F. Hund, 'Zur Deutung der Molekelspektren, III', Zeitschrift für Physik 43 (1927), 805-826, see p. 809, especially footnote 1.
59. 26 For testimony to this effect see, e.g. E. H. Kennard, 'Zur Quantenmechanik einfacher Bewegungstypen', Zeitschrift für Physik 44 (1927), 326-352; F. London, 'Quantentheorie und chemische Bindung', in H. Falkenhagen (ed.), Quantentheorie und Chemie, Leipziger Vorträge 1928 (Leipzig: S. Hirzel, 1928), pp. 59-84, see pp. 61-62, footnote 2; and, in an example to be discussed later at length, F. Hund, 'Zur Deutung der Molekelspektren, III', Zeitschrift für Physik 43 (1927), 805-826, see p. 809, especially footnote 1.
60. 27 Pauli to Heisenberg, 19 October 1926, in op. cit., note 19, p. 344; emphasis in the original.
61. +n, - n' of the perturbation between the left-and right-turning states; ibid., p. 344.
62. +n, - n' of the perturbation between the left-and right-turning states; ibid., p. 344.
63. 29 E. Schrödinger, 'Quantisierung als Eigenwertproblem (Dritte Mitteilung: Störungstheorie, mit Anwendung auf den Starkeffekt der Balmerlinien)', Annalen der Physik 80 (1926), 437-490, especially pp. 478-483. Schrödinger did not use perturbation theory to represent the new eigenfunctions as linear combinations of the old ones.
64. 30 W. Heisenberg, 'Schwankungserscheinungen und Quantenmechanik', Zeitschrift für Physik 40 (1926), 501-506; P. Jordan, 'Über die quantenmechanische Darstellung von Quantensprüngen', Zeitschrift für Physik 40 (1927), 661-666.
65. 30 W. Heisenberg, 'Schwankungserscheinungen und Quantenmechanik', Zeitschrift für Physik 40 (1926), 501-506; P. Jordan, 'Über die quantenmechanische Darstellung von Quantensprüngen', Zeitschrift für Physik 40 (1927), 661-666.
66. 31 Heisenberg to Pauli, 28 October 1926, in op. cit., note 19, p. 351; 4 November 1926, p. 352; the paper was received on 6 November 1926.
67. 32 E. Schrödinger, 'Energieaustausch nach der Quantenmechanik', Annalen der Physik 83 (1927), 956-968.
68. 33 Ibid., p. 959.
69. 34 Heitler and London, op. cit., note 2, p. 456, footnote 1.
70. 35 E. Schrödinger, 'Quantisierung als Eigenwertproblem (Zweite Mitteilung)', Annalen der Physik 79 (1926), 489-527, see p. 511; Schrödinger to Planck, 31 May 1926, in Przibram, op. cit., note 10, p. 10; Schrödinger to Lorentz, 6 June 1926, ibid., pp. 54-55.
71. 35 E. Schrödinger, 'Quantisierung als Eigenwertproblem (Zweite Mitteilung)', Annalen der Physik 79 (1926), 489-527, see p. 511; Schrödinger to Planck, 31 May 1926, in Przibram, op. cit., note 10, p. 10; Schrödinger to Lorentz, 6 June 1926, ibid., pp. 54-55.
72. 35 E. Schrödinger, 'Quantisierung als Eigenwertproblem (Zweite Mitteilung)', Annalen der Physik 79 (1926), 489-527, see p. 511; Schrödinger to Planck, 31 May 1926, in Przibram, op. cit., note 10, p. 10; Schrödinger to Lorentz, 6 June 1926, ibid., pp. 54-55.
73. 36 Heitler later recalled that they had not had close discussions with Schrödinger on their paper; W. Heitler, interview by John L. Heilbron (1963), Archive for History of Quantum Physics.
74. 37 The same can be said as well of Heitler and London's calculational method. One reason why their treatment of the hydrogen molecule, as they actually carried it out, looks rather less familiar than the reconstruction given at the start of this section, was that they closely followed a perturbation scheme laid down not by Dirac, and certainly not by Born, Heisenberg, and Jordan, but by Schrödinger: Dirac, op. cit., note 14; M. Born, W. Heisenberg and P. Jordan, 'Zur Quantenmechanik, II', Zeitschrift für Physik 35 (1926), 557-615; op. cit., note 29. Though this did not indicate any necessary commitment to Schrödinger's program, it at least demonstrated Heitler and London's mastery of his techniques.
75. 37 The same can be said as well of Heitler and London's calculational method. One reason why their treatment of the hydrogen molecule, as they actually carried it out, looks rather less familiar than the reconstruction given at the start of this section, was that they closely followed a perturbation scheme laid down not by Dirac, and certainly not by Born, Heisenberg, and Jordan, but by Schrödinger: Dirac, op. cit., note 14; M. Born, W. Heisenberg and P. Jordan, 'Zur Quantenmechanik, II', Zeitschrift für Physik 35 (1926), 557-615; op. cit., note 29. Though this did not indicate any necessary commitment to Schrödinger's program, it at least demonstrated Heitler and London's mastery of his techniques.
76. 37 The same can be said as well of Heitler and London's calculational method. One reason why their treatment of the hydrogen molecule, as they actually carried it out, looks rather less familiar than the reconstruction given at the start of this section, was that they closely followed a perturbation scheme laid down not by Dirac, and certainly not by Born, Heisenberg, and Jordan, but by Schrödinger: Dirac, op. cit., note 14; M. Born, W. Heisenberg and P. Jordan, 'Zur Quantenmechanik, II', Zeitschrift für Physik 35 (1926), 557-615; op. cit., note 29. Though this did not indicate any necessary commitment to Schrödinger's program, it at least demonstrated Heitler and London's mastery of his techniques.
77. 38 Heitler and London, op. cit., note 2, p. 461; cf. W. Heitler, 'Zur Gruppentheorie der homöopolaren chemischen Bindung', Zeitschrift für Physik 47 (1928), 835-858, see p. 838, n.*. Heitler and London's notion of exchange entailed a switch of electrons between two spatially different states with the same energy, while Heisenberg's resonance concept involved a switch between two states differing primarily in their energy levels.
78. 38 Heitler and London, op. cit., note 2, p. 461; cf. W. Heitler, 'Zur Gruppentheorie der homöopolaren chemischen Bindung', Zeitschrift für Physik 47 (1928), 835-858, see p. 838, n.*. Heitler and London's notion of exchange entailed a switch of electrons between two spatially different states with the same energy, while Heisenberg's resonance concept involved a switch between two states differing primarily in their energy levels.
79. 39 Heitler recalled his acceptance of the Born statistical interpretation as having occurred after the Heitler-London paper was written; op. cit., note 36. This is also of interest for dating the spreading acceptance of transformation theory.
80. 40 F. Hund, 'Zur Deutung der Molekelspektren, I', Zeitschrift für Physik 40 (1927), 742-764; cf. Carsten Jensen, 'Two One-Electron Anomalies in the Old Quantum Theory', Historical Studies in the Physical and Biological Sciences 15 (1984), 81-106.
81. 40 F. Hund, 'Zur Deutung der Molekelspektren, I', Zeitschrift für Physik 40 (1927), 742-764; cf. Carsten Jensen, 'Two One-Electron Anomalies in the Old Quantum Theory', Historical Studies in the Physical and Biological Sciences 15 (1984), 81-106.
82. 41 Heisenberg, who was in Copenhagen with Hund at the time, was very enthusiastic; Heisenberg to Pauli, 28 October 1926, in op. cit., note 19, p. 350.
83. 42 Op. cit., note 40, p. 749.
84. 43 Ibid., p. 745; op. cit., note 23.
85. 43 Ibid., p. 745; op. cit., note 23.
86. 44 Hund, op. cit., note 26. In this later paper Hund was studying mirror-molecules, or pairs of molecules whose arrangements of atoms mirrored one another like a left and a right hand. Formally this degenerate problem was very much like the two-well potential he had studied earlier.
87. 45 Ibid., p. 810; emphasis in the original.
88. α) als die Frequenz zu deuten haben, mit welcher im Mittel ein Austausch der beiden Elektronen erfolgt'; Heitler and London, op. cit, note 2, p. 461.
89. 47 Cf. H. Bethe, 'Quantenmechanik der Ein-und Zwei-Elektronenprobleme', in H. Geiger and Karl Scheel (Eds), Handbuch der Physik, Vol. 24, Part 1, Quantentheorie (Berlin: Julius Springer, 1933), pp. 273-560, see p. 335.
90. α). Again this is wrong, but the error is consistent with the previous one. Heitler, 'Störungsenergie', op. cit., note 8, p. 48.
91. 49 Ibid., 48; London, op. cit., note 26, pp. 64-65. When London returned to the problem, he did not talk about the Austausch of one electron with another.
92. 49 Ibid., 48; London, op. cit., note 26, pp. 64-65. When London returned to the problem, he did not talk about the Austausch of one electron with another.
93. 50 Unfortunately I have not been able to find any archival material relating to this issue.
94. 51 Heitler, 'Störungsenergie', op. cit., note 8; Heitler, 'Elektronenaustausch', op. cit., note 8. Whether Heitler became so interested in exchange during the writing of the Heitler-London paper or afterwards is unclear. London's later papers showed no sign of such an attachment.
95. 51 Heitler, 'Störungsenergie', op. cit., note 8; Heitler, 'Elektronenaustausch', op. cit., note 8. Whether Heitler became so interested in exchange during the writing of the Heitler-London paper or afterwards is unclear. London's later papers showed no sign of such an attachment.
96. 52 Heitler, 'Störungsenergie', op. cit., note 8, see p. 48; emphasis in the original.
97. 53 See, e.g. Linus Pauling and E. Bright Wilson, Jr. Introduction to Quantum Mechanics, With Applications to Chemistry (New York: McGraw-Hill, 1935). It would be interesting to ask whether this approach found more resonance among American physicists and chemists; cf. Gavroglu and Simões, op. cit., note 2; Alexi Assmus. The Americanization of Molecular Physics', Historical Studies in the Physical and Biological Sciences 23 (1992), 1-34; S. S. Schweber, 'The Empiricist Temper Regnant: Theoretical Physics in the United States 1920-1950', Historical Studies in the Physical and Biological Sciences 17 (1986), 55-98.
98. 53 See, e.g. Linus Pauling and E. Bright Wilson, Jr. Introduction to Quantum Mechanics, With Applications to Chemistry (New York: McGraw-Hill, 1935). It would be interesting to ask whether this approach found more resonance among American physicists and chemists; cf. Gavroglu and Simões, op. cit., note 2; Alexi Assmus. The Americanization of Molecular Physics', Historical Studies in the Physical and Biological Sciences 23 (1992), 1-34; S. S. Schweber, 'The Empiricist Temper Regnant: Theoretical Physics in the United States 1920-1950', Historical Studies in the Physical and Biological Sciences 17 (1986), 55-98.
99. 53 See, e.g. Linus Pauling and E. Bright Wilson, Jr. Introduction to Quantum Mechanics, With Applications to Chemistry (New York: McGraw-Hill, 1935). It would be interesting to ask whether this approach found more resonance among American physicists and chemists; cf. Gavroglu and Simões, op. cit., note 2; Alexi Assmus. The Americanization of Molecular Physics', Historical Studies in the Physical and Biological Sciences 23 (1992), 1-34; S. S. Schweber, 'The Empiricist Temper Regnant: Theoretical Physics in the United States 1920-1950', Historical Studies in the Physical and Biological Sciences 17 (1986), 55-98.
100. 53 See, e.g. Linus Pauling and E. Bright Wilson, Jr. Introduction to Quantum Mechanics, With Applications to Chemistry (New York: McGraw-Hill, 1935). It would be interesting to ask whether this approach found more resonance among American physicists and chemists; cf. Gavroglu and Simões, op. cit., note 2; Alexi Assmus. The Americanization of Molecular Physics', Historical Studies in the Physical and Biological Sciences 23 (1992), 1-34; S. S. Schweber, 'The Empiricist Temper Regnant: Theoretical Physics in the United States 1920-1950', Historical Studies in the Physical and Biological Sciences 17 (1986), 55-98.
101. 54 After leaving Zürich for Göttingen, Heitler himself abandoned this point of view. See Sir Nevill Mott, 'Walter Heinrich Heitler', Biographical Memoirs of the Fellows of the Royal Society 28 (1982), 141-151; op. cit., note 36.
102. 54 After leaving Zürich for Göttingen, Heitler himself abandoned this point of view. See Sir Nevill Mott, 'Walter Heinrich Heitler', Biographical Memoirs of the Fellows of the Royal Society 28 (1982), 141-151; op. cit., note 36.
103. 55 See, for instance, op. cit, note 49, pp. 324-326; F. Hund, 'Allgemeine Quantenmechanik des Atom-und Molekelbaues', in Geiger and Scheel (eds), op. cit., note 47, pp. 561-694, see pp. 581-592. Hund's growing concern with symmetries also inclined him to think of exchanges in this way.
104. 55 See, for instance, op. cit, note 49, pp. 324-326; F. Hund, 'Allgemeine Quantenmechanik des Atom-und Molekelbaues', in Geiger and Scheel (eds), op. cit., note 47, pp. 561-694, see pp. 581-592. Hund's growing concern with symmetries also inclined him to think of exchanges in this way.
105. 56 W. Heisenberg, 'Zur Theorie des Ferromagnetismus', Zeitschrift für Physik 49 (1928), 619-636, see p. 620. As early as 1926 Heisenberg already had the idea of explaining the spin-spin coupling of ferromagnetism in this way; Heisenberg to Pauli, 4 November 1926, in op. cit., note 19, p. 353.
106. 56 W. Heisenberg, 'Zur Theorie des Ferromagnetismus', Zeitschrift für Physik 49 (1928), 619-636, see p. 620. As early as 1926 Heisenberg already had the idea of explaining the spin-spin coupling of ferromagnetism in this way; Heisenberg to Pauli, 4 November 1926, in op. cit., note 19, p. 353.
107. 57 P. A. M. Dirac, 'Quantum Mechanics of Many-electron Systems', Royal Society of London, Proceedings A123 (1929), 714-733. The Dirac vector model for magnetic interactions was particularly promoted in J. H. van Vleck, The Theory of Electric and Magnetic Susceptibilities (Oxford: Oxford University Press, 1932), Sections 76 and 77.
108. 57 P. A. M. Dirac, 'Quantum Mechanics of Many-electron Systems', Royal Society of London, Proceedings A123 (1929), 714-733. The Dirac vector model for magnetic interactions was particularly promoted in J. H. van Vleck, The Theory of Electric and Magnetic Susceptibilities (Oxford: Oxford University Press, 1932), Sections 76 and 77.
109. 58 J. R. Oppenheimer, 'On the Quantum Theory of Electronic Impacts', Physical Review 32 (1928), 361-376; cf. Gregor Wentzel, 'Wellenmechanik der Stoß-und Strahlungsvorgänge', in Geiger and Scheel (eds), op. cit., note 47, pp. 695-784, see pp. 726-734.
110. 58 J. R. Oppenheimer, 'On the Quantum Theory of Electronic Impacts', Physical Review 32 (1928), 361-376; cf. Gregor Wentzel, 'Wellenmechanik der Stoß-und Strahlungsvorgänge', in Geiger and Scheel (eds), op. cit., note 47, pp. 695-784, see pp. 726-734.