Anomalies in quantum mechanics: The 1/r2 potential

American Journal of Physics

Volumn 70, Issue 5, 2002, Pages 513-519

  Coon, Sidney A ^a,b   Holstein, Barry R ^c,d  

^a NATIONAL SCIENCE FOUNDATION   (United States)

^b NEW MEXICO STATE UNIVERSITY   (United States)

^c FORSCHUNGSZENTRUM JÜLICH   (Germany)

^d UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23044532619     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1456071     Document Type: Article

References (30)

1. D. Bjorken and S. D. Drell, Relatvistic Quantum Fields (McGraw-Hill, New York, 1985);
2. N. Byers, "E. Noether's discovery of the deep connection between symmetries and conservation laws," physics/9807044.
3. See for example, M. Gell-Mann and Y. Ne'eman, The Eightfold Way (Benjamin, New York, 1964).
4. See for example, B. R. Holstein, Weak Interactions in Nuclei (Princeton U.P., Princeton, 1989).
5. H. Goldstein, "Prehistory of the 'Runge-Lenz' vector," Am. J. Phys. 43, 737-738 (1975);
6. G. Baym, Lectures in Quantum Mechanics (Benjamin, Reading, MA, 1969).
7. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1964), Vol. II, Chap. 36.
8. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1964), Vol. III, Chap. 21.
9. N. Straumann, "Historical and other remarks on hidden symmetries," in Proceedings of the Summer School on Hidden Symmetries and Higgs Phenomena, edited by D. Graudenz (PSI, Villigen, Switzerland, 1998).
10. See, for example, S. B. Treiman, R. Jackiw, B. Zumino, and E. Witten, Current Algebras and Anomalies (World Scientific, Singapore, 1985).
11. See, for example, J. F. Donoghue, E. Golowich, and B. R. Holstein, Dynamics of the Standard Model (Cambridge U.P., New York, 1992), Chap. III.
12. L. R. Mead and J. Godines, "An analytic example of renormalization in two dimensional quantum mechanics," Am. J. Phys. 59, 935 (1991);
13. B. R. Holstein, "Anomalies for pedestrians," ibid. 61, 142-147 (1993).
14. R. Jackiw, "Introducing scale symmetry," Phys. Today 25(1), 23-27 (1972).
15. R. Jackiw, "Delta-function potentials in two- and three-dimensional quantum mechanics," in M. A. B. Beq Memorial Volume, edited by A. Ali and P. Hoodbhoy (World Scientific, Singapore, 1991), pp. 25-42;
16. I. Lapidus, "Quantum-mechanical scattering in two dimensions," Am. J. Phys. 50, 45-47 (1982).
17. Here we follow the approach of H. E. Camblong, L. N. Epele, H. Fan- chiotti, and C. A. Garcia Canal, "Renormalization of the inverse square potential," Phys. Rev. Lett. 85, 1590-1593 (2000);
18. "Dimensional transmutation and dimensional regularization in quantum mechanics. I. General theory," Ann. Phys. (N.Y.) 287, 14-56 (2001);
19. "Dimensional transmutation and dimensional regularization in quantum mechanics. II. Rotational invariance," 287, 57-100 (2001).
20. A. M. Perelomov and V.S. Popov, " 'Fall to the Center' in quantum mechanics," Teor. Mat. Fiz. 4, 48 (1970) [Theor. Math Phys. 4, 664-677 (1970)].
21. 2 potential," Am. J. Phys.42, 960-964 (1974).
22. H. E. Camblong, L. N. Epele, H. Fanchiotti, and C. A. Garcia Canal,"Quantum anomaly in molecular physics," Phys. Rev. Lett. 87, 220402 (2001).
23. C. Desfrancois, H. Abdoul-Carime, N. Khelifa, and J. P. Schermann, "From 1/r to 1/2, potentials: Electron exchange between Rydberg atoms and polar molecules," Phys. Rev. Lett. 73, 2436-2439 (1994);
24. J.-M. Levy- Leblond, "Electron capture by polar molecules," Phys. Rev. 153, 1-4 (1967).
25. J. Denschlag, G. Umshaus, and J. Schmiedmayer, "Probing a singular potential with cold atoms: A neutral atom and a charged wire," Phys. Rev.Lett. 81, 737-741 (1998).
26. 2 potential," J. Math. Phys. 16, 544-547 (1975).
27. M. Bawin and S. A. Coon, "A neutral atom and a charged wire: From elastic scattering to absorption," Phys. Rev. A 63, 1-3 (2001).
28. For a review, see, for example, V. Efimov, "Is a qualitative approach to the three-body problem useful?," Comments Nucl. Part. Phys. 19, 271-294 (1990).
29. P. F. Bedaque, H.-W. Hammer, and U. Van Kolck, "The three-boson system with short-range interactions," Nucl. Phys. A 646, 444-466 (1999);
30. "Effective theory of the triton," 676, 357-370 (2000).