文献类型：期刊文献

英文题名：Qiang-Dong proper quantization rule and its applications to exactly solvable quantum systems

作者：Serrano, F. A.[1];Gu, Xiao-Yan[2];Dong, Shi-Hai[3]

机构：[1]Inst Politecn Nacl, Mexico City 04430, DF, Mexico;[2]E China Univ Sci & Technol, Dept Phys, Shanghai 200237, Peoples R China;[3]Inst Politecn Nacl, Escuela Super Fis & Matemat, Unidad Profes Adolfo Lopez Mateos, Mexico City 07738, DF, Mexico

年份：2010

卷号：51

期号：8

外文期刊名：JOURNAL OF MATHEMATICAL PHYSICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000281905000003)】；

基金：We would like to thank the kind referee for making invaluable and positive suggestions which have improved the present manuscript greatly. This work is dedicated to Professor Zhong-Qi Ma on the occasion of his 70th birthday. This work was supported by the NNSF of China (Project No. 10905022) and partly by COFAA-IPN, Mexico Grant No. 200100297-SIP-IPN.

语种：英文

摘要：We propose proper quantization rule, integral(xB)(xA)k(x)dx- integral(x0B)(x0A)k(0)(x)dx=n pi, where k(x) =root 2M[E-V(x)]/h. The x(A) and x(B) are two turning points determined by E=V(x), and n is the number of the nodes of wave function Psi(x). We carry out the exact solutions of solvable quantum systems by this rule and find that the energy spectra of solvable systems can be determined only from its ground state energy. The previous complicated and tedious integral calculations involved in exact quantization rule are greatly simplified. The beauty and simplicity of the rule come from its meaning whenever the number of the nodes of phi(x) or the number of the nodes of the wave function Psi(x) increases by 1, the momentum integral integral(xB)(xA)k(x)dx will increase by pi. We apply this proper quantization rule to carry out solvable quantum systems such as the one-dimensional harmonic oscillator, the Morse potential and its generalization, the Hulthen potential, the Scarf II potential, the asymmetric trigonometric Rosen-Morse potential, the Poschl-Teller type potentials, the Rosen-Morse potential, the Eckart potential, the harmonic oscillator in three dimensions, the hydrogen atom, and the Manning-Rosen potential in D dimensions. (C) 2010 American Institute of Physics. [doi :10.1063/1.3466802]