On coherent-state representations of quantum mechanics: Wave mechanics in phase space

Journal of Chemical Physics

Volumn 106, Issue 17, 1997, Pages 7228-7240

  Møiler, Klaus B ^a   Jørgensen, Thomas G ^a   Torres Vega, Gabino ^b  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b DEPARTAMENTO DE FÍSICA   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038246362     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.473684     Document Type: Article

References (40)

1. V. Fock, Z. Phys. 49, 339 (1928).
2. V. Bargmann, Commun. Pure Appl. Math 14, 187 (1961).
3. E. Wigner, Phys. Rev. 40, 749 (1932).
4. K. Husimi, Proc. Phys. Math. Soc. Jpn. 22, 264 (1940).
5. J. R. Klauder and B.-S. Skagerstam, Coherent States (World Scientific, Singapore, 1985).
6. A. Perelomov, Generalized Coherent States and Their Applications: Texts and Monographs in Physics (Springer Verlag, Berlin, 1986).
7. M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984).
8. J. E. Harriman and M. E. Casida, Int. J. Quantum Chem. 45, 263 (1993).
9. M. V. Berry, Philos. Trans. R. Soc. London, Ser. A 287, 237 (1977).
10. K, Takahashi, J. Phys. Soc. Jpn. 55, 762 (1986).
11. A. Voros, Phys. Rev. A 40, 6814 (1989).
12. Go. Torres-Vega and J. H. Frederick, J. Chem. Phys. 98, 3103 (1993).
13. Go. Torres-Vega, J. Chem. Phys. 98, 7040 (1993).
14. Go. Torres-Vega, J. Chem. Phys. 99, 1824 (1993).
15. Go. Torres-Vega, in Third International Workshop on Squeezed States and Uncertainty Relations, edited by D. Ban, Y. S. Kim, N. M. Rubin, Y. Shih, and W. W. Zachary (NASA, Maryland, 1994), pp. 275-280.
16. Go. Torres-Vega and J. D. Morales-Guzmán, J. Chem. Phys. 101, 5847 (1994).
17. Go. Torres-Vega, A. Zúñiga-Segundo, and J. D. Morales-Guzmán, Phys. Rev. A 53, 3792 (1996).
18. R. J. Glauber, Phys. Rev. 130, 2529 (1963).
19. J. E. Harriman, J. Chem. Phys. 100, 3651 (1994).
20. Go. Torres-Vega and J. H. Frederick, J. Chem. Phys. 93, 8862 (1990).
21. P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Oxford University Press, Oxford, 1958).
22. J. J. Wlodarz, J. Chem. Phys. 100, 7476 (1994).
23. J. E. Harriman, J. Chem. Phys. 88, 6399 (1988).
24. S. Stenholm, Eur. J. Phys. 1, 244 (1980).
25. A. Royer, Phys. Rev. Lett. 55, 2745 (1985).
26. For a discussion of simultaneous measurements of non-commuting observables in terms of the precise mathematical concepts "fuzzy sets" and "fuzzy measures," see e.g., E. Prugoveôki, Found. Phys. 3, 3 (1973) and E. B. Davies and J. T. Lewis, Commun. Math. Phys. 17, 239 (1970).
27. For a discussion of simultaneous measurements of non-commuting observables in terms of the precise mathematical concepts "fuzzy sets" and "fuzzy measures," see e.g., E. Prugoveôki, Found. Phys. 3, 3 (1973) and E. B. Davies and J. T. Lewis, Commun. Math. Phys. 17, 239 (1970).
28. This should be compared with, for instance, the position-space representation where the square magnitude of the wave function can be used to calculate the expectation value of any operator that is a function of the position operator. This is due to the fact that any such operator is multiplicative in the position-space representation. Since neither the position nor the momentum operator is multiplicative in a CSR it is not obvious whether the square magnitude of the phase-space wave function can be used in a similar way.
29. P. Meystre and M. Sargent III, Elements of Quantum Optics, 2nd ed. (Springer-Verlag, Berlin, 1991).
30. J. P. Dahl, in Classical and Quantum Systems: Foundations and Symmetries, Proceedings of the II International Wigner Symposium, edited by H. D. Doebner, W. Scherer, and F. Schroeck, Jr. (World Scientific, Singapore, 1993), pp. 420-423.
31. J. P. Dahl, in Conceptual Trends in Quantum Chemistry, edited by E. S. Kryachko and J. L. Calais (Kluwer Academic Publishers, Amsterdam, 1994), pp. 199-226.
32. K. E. Cahill and R. J. Glauber, Phys. Rev. 177, 1882 (1969).
33. R. T. Skodje, H. W. Rohrs, and J. VanBuskirk, Phys. Rev. A 40, 2894 (1989).
34. R. J. Glauber, Phys. Rev. 131, 2766 (1963).
35. L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Vol. 3 of Course of Theoretical Physics, 3rd ed. (Pergamon Press Ltd., Oxford, 1977).
36. D. Zwillinger, Handbook of Differential Equations (Academic, San Diego, 1989).
37. K. B. Møller, T. G. Jørgensen, and J. P. Dahl, Phys. Rev. A 54, 5378 (1996).
38. This should be contrasted with the Wigner density which always behaves classically in the potential Eq. (67).
39. J. R. Klauder, in Workshop on Harmonic Oscillators, edited by D. Han, Y. S. Kim, and W. Zachary (NASA, Maryland, 1993), pp. 19-28.
40. The analysis of Klauder only involves the explicit (Latin small letter h with stroke sign) dependence in the equations of motion and is therefore appropriate if the (Latin small letter h with stroke sign) dependence of the initial phase-space density is ignored. See also Ref. 32.