Quantum correspondence for linear canonical transformations on general Hamiltonian systems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 58, Issue 3, 1998, Pages 1765-1774

  Yeon, Kyu Hwang ^a   Walls, Dan F ^a   Um, Chung In ^b   George, Thomas F ^c   Pandey, Lakshmi N ^d  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b Korea University   (South Korea)

^c UNIVERSITY OF WISCONSIN STEVENS POINT   (United States)

^d GEORGIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000832697     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.58.1765     Document Type: Article

References (22)

1. E. C. G. Sudarshan and N. Mukunda, Classical Dynamics: A Modern Perspective (Wiley, New York, 1974);
2. H. Goldstein, Classical Mechanics (Addision-Wesley, Reading, Massachusetts, 1980).
3. R. Shankar, Principles of Quantum Mechanics (Plenum, New York, 1994);
4. J. J. Sakurai, Modern Quantum Mechanics (Addision-Wesley, Reading, Massachusetts, 1994).
5. K. H. Yeon, D. H. Kim, C. I. Um, T. F. George, and L. N. Pandey, Phys. Rev. A 55, 4023 (1997).PLRAAN
6. L. F. Landovitz and A. M. Levine, Phys. Rev. A 20, 1162 (1979); PLRAAN
7. L. F. Landovitz, A. M. Levine, and W. H. Shreiber, J. Math. Phys. 21, 2159 (1980).JMAPAQ
8. V. V. Dodonov and V. I. Man’ko, Phys. Rev. A 20, 550 (1979).PLRAAN
9. L. S. Brown, Phys. Rev. Lett. 66, 527 (1991).PRLTAO
10. D. M. Greenberger, J. Math. Phys. 20, 762,771 (1979).JMAPAQ
11. M. Sebawe Abdalla and R. K. Colegrave, Phys. Rev. A 32, 1958 (1985); PLRAAN
12. M. Sebawe AbdallaR. K. ColegraveJ. Phys. A15, 1549 (1982).
13. C. I. Um, K. H. Yeon, and W. H. Kahng, J. Phys. A 20, 611 (1987); JPHAC5
14. K. H. Yeon, C. I. Um, and T. F. George, Phys. Rev. A 36, 5287 (1987).PLRAAN
15. D. C. Khandekar and S. V. Lawande, J. Math. Phys. 16, 384 (1975).JMAPAQ
16. The (Formula presented) term is not inserted in Eq. (4) since it makes the arbitrary potential term difficult to treat. We may discuss our problem including the (Formula presented) term if the potential is fixed.
17. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965);
18. W. Dittrich and M. Reuter, Classical and Quantum Dynamics (Springer-Verlag, Berlin, 1993);
19. D. C. Khandekar, S. V. Lawande, and K. V. Bhagwat, Path Integral Methods and Their Applications (World Scientific, Singapore, 1993);
20. L. S. Schulman, The Techniques and Applications of Path Integration (Wiley, New York, 1981).
21. L. Chetouani, L. Guechi, and T. F. Hammann, Phys. Rev. A 40, 1157 (1989).PLRAAN
22. The frequency of the damped harmonic oscillator depends on the damping constant and is different than the frequency of the harmonic oscillator when the damping constant approaches zero.