Discovering by analogy: The case of Schrödinger's equation

European Journal of Physics

Volumn 19, Issue 1, 1998, Pages 69-75

  Tzanakis, Constantinos ^a  

^a UNIVERSITY OF CRETE   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0009618621     PISSN: 01430807     EISSN: None     Source Type: Journal    
DOI: 10.1088/0143-0807/19/1/010     Document Type: Article

References (49)

1. Beem J K and Ehrlich P E 1981 Global Lorentzian Geometry (New York: Dekker) chs 10, 11
2. Bekenstein J 1973 Phys. Rev. D 7 2333 (particularly section II)
3. Bekenstein J 1974 Phys. Rev. D 12 3992
4. Brousseau G 1983 Recherche en Didactique des Mathématiques 4 (165) 193
5. Brush S G 1983 Statistical Physics and the Atomic Theory of Matter (Princeton, NJ: Princeton University Press) pp 131-2
6. de Broglie L 1927 Ann. Phys., Paris 3 22
7. Choquet-Bruhat Y, de Witt-Morette C and Dillard-Bleick M 1982 Analysis, Manifolds and Physics (Amsterdam: North-Holland) ch II.A
8. Courant R and Hubert D 1962 Methods of Mathematical Physics vol II (New York: Wiley) section II.9.2
9. Dugas R 1988 A history of mechanics (New York: Dover) part IV, ch VI
10. Edwards H M 1977 Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory (Berlin: Springer)
11. Goldstein G 1980 Classical Mechanics (Reading, MA: Addison-Wesley)
12. Hairer E and Wanner G 1996 Analysis by its History (Berlin: Springer)
13. Halmos P R 1950 Measure Theory (New York: Van Nostrand) ch V
14. Hawking S W 1975 Commun. Math. Phys. 43 199
15. Hawking S W and Ellis G F R 1973 The Large-scale Structure of Spacetime (Cambridge: Cambridge University Press) ch 8
16. Hawking S W and Penrose R 1996 The Nature of Space and Time (Princeton, NJ: Princeton University Press) pp 29-30
17. Heisenberg W 1949 The Physical Principles of the Quantum Theory (New York: Dover) appendix
18. Jammer M 1965 The Conceptual Development of Quantum Mechanics (London: McGraw-Hill) section 5.3 (particularly pp 257-8)
19. Klein F 1979 Development of Mathematics in the 19th Century (Brookline, MA: Mathematics and Science Press). Originally published as: 1928 Vorlesungen uber die Entwicklung der Mathematik im 19 Jahrhundert (Berlin: Springer)
20. Klein F 1979 Development of Mathematics in the 19th Century (Brookline, MA: Mathematics and Science Press). Originally published as: 1928 Vorlesungen uber die Entwicklung der Mathematik im 19 Jahrhundert (Berlin: Springer)
21. Kragh H 1982 Centaurus 26 154
22. _ 1990 Dirac: A Scientific Biography (Cambridge: Cambridge University Press) pp 49-51
23. Landau L and Lifchitz E 1969 Électrodynamique des milieux continus (Moscow: MIR) ch X
24. Mehra J and Rechenberg H 1987 The Historical Development of Quantum Theory vol 5 (Berlin: Springer)
25. Naber G L 1987 Spacetime and Singularities (Cambridge: Cambridge University Press) ch 4, p VIII
26. O' Neill B 1983 Semi-Riemannian Geometry (New York: Academic Press) ch 14
27. Pais A 1991 Niels Bohr's Times (Oxford: Oxford University Press) section 14(b)
28. Pauli W 1973 Optics and the Theory of Electrons (Cambridge MA: MIT Press) ch I
29. Polya G 1954 Induction and Analogy in Mathematics (Princeton, NJ: Princeton University Press) preface
30. _ 1968 Patterns of Plausible Inference (Princeton, NJ: Princeton University Press) ch XV
31. Rüdinger E 1976 Am. J. Phys. 44 144
32. Schrödinger E 1982 Wave Mechanics (New York: Chelsea) paper II, lecture I. Paper II originally published as: 1926 Ann. Phys. (4) 79; lecture I originally published as: 1928 Four Lectures on Wave Mechanics (Glasgow)
33. Schrödinger E 1982 Wave Mechanics (New York: Chelsea) paper II, lecture I. Paper II originally published as: 1926 Ann. Phys. (4) 79; lecture I originally published as: 1928 Four Lectures on Wave Mechanics (Glasgow)
34. Schrödinger E 1982 Wave Mechanics (New York: Chelsea) paper II, lecture I. Paper II originally published as: 1926 Ann. Phys. (4) 79; lecture I originally published as: 1928 Four Lectures on Wave Mechanics (Glasgow)
35. Schumbring G 1977 Zentralblatt für Didaktik der Mathematik 9 (209) 211
36. Sierpinska A 1991 Cahiers de didactique des Mathématiques 7 (11) 13
37. Sommerfeld A 1964 Optics (New York: Academic) section 35.A, footnote to p 207
38. Toeplitz O 1963 Calculus: A Genetic Approach (Chicago, IL: Chicago University Press)
39. Tomonaga S I 1962 Quantum Mechanics vol I (Amsterdam: North-Holland)
40. _ 1966 Quantum Mechanics vol II (Amsterdam: North-Holland)
41. Tzanakis C 1993 Proc. 1st European Summer University on History and Epistemology in Mathematics Education ed F Lalande, F Jaboeuf and Y Nouazé (Montpellier: IREM de Montpellier) p 271
42. _ 1995 Int. J. Math. Education Sci. Techn. 26 45
43. _ 1996 Proc. 2nd European Summer University on History and Epistemology in Mathematics Education vol II ed M J Lagarto, A Vieira and E Veloso (Braga, Portugal: Universidade do Minho) p 96
44. _ 1997a Proc. 2nd World Congress of Nonlinear Analysts ed V Lakshmikantham (Amsterdam: Elsevier) to be published
45. _ 1997b Presenting the relation between Mathematics and Physics on the basis of their history: a genetic approach Using History of Mathematics in Teaching Mathematics ed V Katz (Washington, DC: The Mathematical Association of America) to be published
46. Tzanakis C and Coutsomitros C 1988 Eur. J. Phys. 9 276
47. van der Waerden 1967 Sources of Quantum Mechanics (New York: Dover) ch 12 (particularly section 1)
48. Wald R 1984 General Relativity (Chicago, IL: Chicago University Press)
49. Yourgrau W and Mandelstam S 1968 Variational Principles in Dynamics and Quantum Theory (Philadelphia, PA: Saunders)