Proper quantization rule

被引:120
作者
Qiang, Wen-Chao [1 ]
Dong, Shi-Hai [2 ]
机构
[1] Xian Univ Architecture & Technol, Fac Sci, Xian 710055, Peoples R China
[2] Inst Politecn Nacl, Dept Fis, Escuela Super Fis & Matemat, Mexico City 07738, DF, Mexico
关键词
POTENTIALS;
D O I
10.1209/0295-5075/89/10003
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We find a proper quantization rule, integral(xB)(xA) k(x)dx - integral(x0B)(x0A) k(0)(x)dx = n pi, where n is the number of the nodes of wave function psi(x). By this rule the energy spectra of a solvable system can be determined from its ground-state energy only. Particularly, we study three solvable quantum systems-modified Rosen-Morse potential, symmetric trigonometric Rosen-Morse potential and Manning-Rosen potential in D dimensions-with the proper quantization rule, and show that the previous complicated and tedious calculations can be greatly simplified. This proper quantization rule applies to any exactly solvable potential, and one can easily obtain its energy spectra with the rule.
引用
收藏
页数:4
相关论文
共 19 条
[1]  
[Anonymous], 1988, Special functions of mathematical physics
[2]  
[Anonymous], 1968, QUANTUM MECH
[3]  
COOPER F, 1995, PHYS REP, V251, P268
[4]  
Dong S.H., 2007, Factorization Method in Quantum Mechanics, V150, DOI DOI 10.1007/978-1-4020-5796-0
[5]   Energy spectra of the hyperbolic and second Poschl-Teller like potentials solved by new exact quantization rule [J].
Dong, Shi-Hai ;
Gonzalez-Cisneros, A. .
ANNALS OF PHYSICS, 2008, 323 (05) :1136-1149
[6]   Bohr-Sommerfeld quantization of spin Hamiltonians [J].
Garg, A ;
Stone, M .
PHYSICAL REVIEW LETTERS, 2004, 92 (01) :4
[7]   The improved quantization rule and the Langer modification [J].
Gu, Xiao-Yan ;
Dong, Shi-Hai .
PHYSICS LETTERS A, 2008, 372 (12) :1972-1977
[8]   Energy spectra for modified Rosen-Morse potential solved by the exact quantization rule [J].
Gu, Xiao-Yan ;
Dong, Shi-Hai ;
Ma, Zhong-Qi .
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2009, 42 (03)
[9]   Accuracy of semiclassical methods for shape-invariant potentials [J].
Hruska, M ;
Keung, WY ;
Sukhatme, U .
PHYSICAL REVIEW A, 1997, 55 (05) :3345-3350
[10]   Bohr-Sommerfeld quantization condition for the Gross-Pitaevskii equation [J].
Konotop, VV ;
Kevrekidis, PG .
PHYSICAL REVIEW LETTERS, 2003, 91 (23)