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http://dx.doi.org/10.5012/bkcs.2012.33.3.818

Langer Modification in WKB Quantization for Translationally Shape Invariant Potentials  

Sun, Ho-Sung (Department of Chemistry, Sungkyunkwan University)
Publication Information
Bulletin of the Korean Chemical Society / v.33, no.3, 2012 , pp. 818-824 More about this Journal
Abstract
When the Langer modification is applied to Coulomb potential, the standard WKB quantization yields an exact energy spectrum for the potential. This Langer modification has been known to be related to the centrifugal term appearing in Coulomb potential. But we find that a similar modification exists for all translationally shape invariant potentials without referring to the centrifugal term. The characteristic shape of the potentials accounts for the generalized version of Langer modification that makes the WKB quantization valid for all translationally shape invariant potentials.
Keywords
WKB quantization; Langer modification; Shape invariant potentials;
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  • Reference
1 Sergeenko, M. N. Phys. Rev. A 1996, 53, 6.
2 Cooper, F.; Khare, A.; Sukhatme, U. Phys. Rep. 1995, 251, 267.   DOI
3 Yin, C.; Cao, Z. Ann. Phys. 2010, 325, 528.   DOI
4 Barclay, D. T. Phys. Lett. A 1994, 185, 169.   DOI
5 Natanzon, G. A. Teoret. Mat. Fiz. 1979, 38, 146.   DOI   ScienceOn
6 Ginocchio, J. N. Ann. Phys. 1984, 152, 203.   DOI
7 Cooper, F.; Ginocchio, J. N. Phys. Rev. D 1987, 36, 2458.   DOI
8 Barclay, D. T.; Maxwell, C. J. Phys. Lett. A 1991, 157, 357.   DOI
9 Gedenshtein, L. JETP Lett. 1983, 38, 356.
10 Grandati, Y.; Berard, A. Ann. Phys. 2010, 325, 1235.   DOI
11 Ou, F. C.; Cao, Z. Q.; Shen, Q. S. J. Chem. Phys. 2004, 121, 8175.   DOI
12 Moritz, M. J.; Eltschka, C.; Friedrich, H. Phys. Rev. A 2001, 63, 042102.   DOI
13 Ma, Z. Q.; Xu, B. W. Int. J. Modern Phys. E 2005, 14, 599.   DOI
14 Ma, Z. Q.; Xu, B. W. Europhys. Lett. 2005, 69, 685.   DOI
15 Grandati, Y.; Bérard, A. Phys. Lett. A 2011, 375, 390.   DOI
16 Qiang, W. C.; Dong, S. H. Europhys. Lett. 2010, 89, 10003.   DOI
17 Dong, S. H.; Morales, D.; García-Ravelo, J. Int. J. Modern Phys. E 2007, 16, 189.   DOI
18 Young, L. A.; Uhlenbeck, G. E. Phys. Rev. 1930, 36, 1158.
19 Langer, R. E. Phys. Rev. 1937, 51, 669.   DOI
20 Kang, J. S.; Schnitzer, H. J. Phys. Rev. D 1975, 12, 841.   DOI
21 Berry, M. V.; Mount, K. E. Rep. Prog. Phys. 1972, 35, 315.   DOI
22 Landau, L. D.; Lifshitz, E. M. Quantum Mechanics; Pergamon: Oxford, 1965.
23 Friedrich, H.; Trost, J. Phys. Rev. Lett. 1996, 26, 4869.
24 Hur, J.; Lee, C. Ann. Phys. 2003, 305, 28.   DOI
25 Friedrich, H.; Trost, J. Phys. Rev. A 1999, 59, 1683.   DOI
26 Hainz, J.; Grabert, H. Phys. Rev. A 1999, 60, 1968
27 Flugge, S. Practical Quantum Mechanics I; Springer-Verlag: Berlin, 1971.
28 M. N. Phys. At. Nucl. 1993, 56, 365.
29 Gu, X.; Dong, S. Phys. Lett. A 2008, 372, 1972.   DOI
30 Wentzel, G. Z. Physik 1926, 38, 518.   DOI
31 Kramers, H. A. Z. Physik 1926, 39, 828.   DOI
32 Brillouin, L. C. R. Hebd. Acad. Sci. 1926, 183, 24.
33 Froman, N.; Froman, P. O. JWKB Approximation; North Holland: Amsterdam, 1965.
34 Merzbacher, E. Quantum Mechanics; Wiley: New York, 1970
35 Friedrich, H.; Trost, J. Phys. Rep. 2004, 397, 359.   DOI