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

Chang Yuan Chen; Fa Lin Lu; Dong Sheng Sun; Shi Hai Dong

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

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

Chang Yuan Chen, Fa Lin Lu, Dong Sheng Sun, Shi Hai Dong

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

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.

Original language	English
Article number	100302
Journal	Chinese Physics B
Volume	22
Issue number	10
DOIs	https://doi.org/10.1088/1674-1056/22/10/100302
State	Published - Oct 2013

Keywords

double ring-shaped Coulomb potential
functional analysis method
super-universal associated-Legendre polynomial

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10.1088/1674-1056/22/10/100302

Cite this

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title = "Analytic solutions of the double ring-shaped Coulomb potential in quantum mechanics",

abstract = "The exact solutions of the Schr{\"o}dinger 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.",

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author = "Chen, {Chang Yuan} and Lu, {Fa Lin} and Sun, {Dong Sheng} and Dong, {Shi Hai}",

year = "2013",

month = oct,

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AU - Lu, Fa Lin

AU - Sun, Dong Sheng

AU - Dong, Shi Hai

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AB - 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.

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KW - functional analysis method

KW - super-universal associated-Legendre polynomial

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DO - 10.1088/1674-1056/22/10/100302

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VL - 22

JO - Chinese Physics B

JF - Chinese Physics B

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

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Keywords

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