Analytic solutions of the double ring-shaped Coulomb potential in quantum mechanics

doi:10.1088/1674-1056/22/10/100302

中国物理B ›› 2013, Vol. 22 ›› Issue (10): 100302-100302.doi: 10.1088/1674-1056/22/10/100302

Analytic solutions of the double ring-shaped Coulomb potential in quantum mechanics

陈昌远^a, 陆法林^a, 孙东升^a, 董世海^b

a School of Physics and Electronics, Yancheng Teachers University, Yancheng 224051, China;
b Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, Mexico D. F. 07738, Mexico

收稿日期:2013-02-17 修回日期:2013-04-10 出版日期:2013-08-30 发布日期:2013-08-30
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11275165), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010291), and partly by Secretaria de Investigacióny Posgrado de Instituto Politécnico Nacional, Mexico (Grant No. 20131150-SIP-IPN).

Analytic solutions of the double ring-shaped Coulomb potential in quantum mechanics

Chen Chang-Yuan (陈昌远)^a, Lu Fa-Lin (陆法林)^a, Sun Dong-Sheng (孙东升)^a, Dong Shi-Hai (董世海)^b

a School of Physics and Electronics, Yancheng Teachers University, Yancheng 224051, China;
b Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, Mexico D. F. 07738, Mexico

Received:2013-02-17 Revised:2013-04-10 Online:2013-08-30 Published:2013-08-30
Contact: Chen Chang-Yuan E-mail:yctcccy@163.net
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11275165), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010291), and partly by Secretaria de Investigacióny Posgrado de Instituto Politécnico Nacional, Mexico (Grant No. 20131150-SIP-IPN).

摘要/Abstract

摘要： The exact solutions of the Schrödinger equation with the double ring-shaped Coulomb potential are presented, including the bound states, continuous states on the “κ/2π scale”, and the calculation formula of the phase shifts. The polar angular wave functions are expressed by constructing the so-called super-universal associated Legendre polynomials. Some special cases are discussed in detail.

关键词: double ring-shaped Coulomb potential, super-universal associated-Legendre polynomial, functional analysis method

Abstract: The exact solutions of the Schrödinger equation with the double ring-shaped Coulomb potential are presented, including the bound states, continuous states on the “κ/2π scale”, and the calculation formula of the phase shifts. The polar angular wave functions are expressed by constructing the so-called super-universal associated Legendre polynomials. Some special cases are discussed in detail.

Key words: double ring-shaped Coulomb potential, super-universal associated-Legendre polynomial, functional analysis method

中图分类号: (Functional analytical methods)

03.65.Db

03.65.Ge (Solutions of wave equations: bound states) 03.65.Nk (Scattering theory)

陈昌远, 陆法林, 孙东升, 董世海. Analytic solutions of the double ring-shaped Coulomb potential in quantum mechanics[J]. 中国物理B, 2013, 22(10): 100302-100302.

Chen Chang-Yuan (陈昌远), Lu Fa-Lin (陆法林), Sun Dong-Sheng (孙东升), Dong Shi-Hai (董世海). Analytic solutions of the double ring-shaped Coulomb potential in quantum mechanics[J]. Chin. Phys. B, 2013, 22(10): 100302-100302.

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Analytic solutions of the double ring-shaped Coulomb potential in quantum mechanics

Analytic solutions of the double ring-shaped Coulomb potential in quantum mechanics

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