Unified approach for exactly solvable potentials in quantum mechanics using shift operators

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 62, Issue 5, 2000, Pages 052110-052111

  Ge, Mo Lin ^a   Kwek, L C ^b   Liu, Yong ^a,b,c   Oh, C H ^b   Wang, Xiang Bin ^b  

^a NANKAI UNIVERSITY   (China)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^c INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; ELECTRIC POTENTIAL; GROUND STATE; MATHEMATICAL TRANSFORMATIONS; MOLECULAR VIBRATIONS; NONLINEAR EQUATIONS; OSCILLATORS (ELECTRONIC); TRANSPORT PROPERTIES; WAVE EQUATIONS;

HARMONIC OSCILLATORS; SHIFT OPERATORS; SOLVABLE POTENTIALS;

QUANTUM THEORY;

EID: 4244189723     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.62.052110     Document Type: Article

References (34)

1. P. Morse, Phys. Rev. 34, 57 (1929).
2. M. Benedict and B. Molnár, Phys. Rev. A 60, R1737 (1999).
3. I. L. Cooper and R. K. Gupta, Phys. Rev. A 52, 941 (1995).
4. R. K. Gupta and I. L. Cooper, J. Phys. A 27, 7811 (1994).
5. A. A. Zembekov, Phys. Rev. A 42, 7163 (1990).
6. M. G. A. Crawford and E. R. Vrsay, Phys. Rev. A 57, 106 (1998).
7. J. L. Chen, Y. Liu, and M. L. Ge, J. Phys. A 31, 6473 (1998).
8. C. Quesne, J. Phys. A 32, 6705 (1999).
9. J. I. Díaz, J. Negro, L. M. Nieto, and O. Rosas-Ortiz, J. Phys. A 32, 8447 (1999).
10. J. Hoppe, Lectures on Integrable Systems (Springer-Verlag, Berlin, 1992).
11. O. L. De Lange and R. E. Raab, Operator Methods in Quantum Mechanics (Clarendon Press, Oxford, 1991).
12. S. Codriansky, P. Cordero, and S. Salamó, J. Phys. A 32, 6287 (1999).
13. F. Cooper, A. Khare, and U. Sukhatme, Phys. Rep. 251, 267 (1995).
14. I. Gendenstein, JETP Lett. 38, 356 (1983).
15. R. Dutt, A. Khare, and U. Sukhatme, Phys. Lett. B 181, 295 (1986).
16. F. Cooper, J. N. Ginocchio, and A. Wipf, Phys. Lett. A 129, 145 (1988).
17. A. Khare and U. Sukhatme, J. Phys. A 21, L501 (1988).
18. J. Dabrowska, A. Khare, and U. Sukhtame, J. Phys. A 21, L195 (1988).
19. G. A. Natanzon, Teor. Mat. Fiz. 38, 146 (1979).
20. T. Fukui and N. Aizawa, Phys. Lett. A 180, 308 (1993).
21. G. Lévai, in Quantum Inversion Theory and Applications, Lecture Notes in Physics No. 488, edited by H. V. von Geramb (Springer-Verlag, Berlin, 1994).
22. Note that there also exist nonshaped invariant Natanzon potentials [13,21].
23. N. Kamran and P. J. Olver, J. Math. Anal. Appl. 145, 342 (1990).
24. K. Celeghini, P. Magnolley, M. Tarlini, and G. Vitiello, Phys. Lett. 162B, 133 (1985).
25. V. Spiridonov, Phys. Rev. Lett. 69, 398 (1992).
26. M. M. Nieto and L. M. Simmons, Jr., Phys. Rev. Lett. 41, 207 (1978); Phys. Rev. D 20, 1321 (1979).
27. M. M. Nieto and L. M. Simmons, Jr., Phys. Rev. Lett. 41, 207 (1978); Phys. Rev. D 20, 1321 (1979).
28. R. F. Wehrhahn, J. Math. Phys. 33, 174 (1992).
29. G. Lévai, Phys. Lett. A 264, 117 (1999); L. C. Kwek, Y. Liu, C. H. Oh, and X. B. Wang (unpublished).
30. G. Lévai, Phys. Lett. A 264, 117 (1999); L. C. Kwek, Y. Liu, C. H. Oh, and X. B. Wang (unpublished).
31. G. Herzberg, Molecular Spectra and Molecular Structure: I Spectra of Diatomic Molecules (Van Nostrand Reinhold, New York, 1950).
32. T. Müller, P. Duprè, P. H. Vaccaro, F. Pérez-Bernal, M. Ibrahim, and F. Iachello, Chem. Phys. Lett. 292, 243 (1998).
33. M. Carvajal, J. M. Arias, and J. Gómez-Camacho, Phys. Rev. A 59, 3462 (1999).
34. F. Iachello and M. Ibrahim, J. Chem. Phys. 102, 9427 (1998).