Exactly complete solutions of the Coulomb potential plus a new ring-shaped potential

Chang Yuan Chen; Shi Hai Dong

doi:10.1016/j.physleta.2004.12.062

Exactly complete solutions of the Coulomb potential plus a new ring-shaped potential

Chang Yuan Chen, Shi Hai Dong

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

110 Scopus citations

Abstract

A new exactly solvable ring-shaped potential is proposed. The energy eigenvalues and eigenfunctions of the bound states for the Schrödinger equation with this potential are presented analytically. The exact solutions of the continuous states of this quantum system are also obtained. The calculation formula of phase shifts is derived. Analytical properties of the scattering amplitude are discussed. We find that the energy of the particle and the radial wave functions of continuous states reduce to the energy eigenvalues and the radial wave functions of the bound states at the poles of the scattering amplitude.

Original language	English
Pages (from-to)	374-382
Number of pages	9
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	335
Issue number	5-6
DOIs	https://doi.org/10.1016/j.physleta.2004.12.062
State	Published - 21 Feb 2005
Externally published	Yes

Keywords

Bound states
Continuous states
Ring-shaped potential
Scattering amplitudes

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10.1016/j.physleta.2004.12.062

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title = "Exactly complete solutions of the Coulomb potential plus a new ring-shaped potential",

abstract = "A new exactly solvable ring-shaped potential is proposed. The energy eigenvalues and eigenfunctions of the bound states for the Schr{\"o}dinger equation with this potential are presented analytically. The exact solutions of the continuous states of this quantum system are also obtained. The calculation formula of phase shifts is derived. Analytical properties of the scattering amplitude are discussed. We find that the energy of the particle and the radial wave functions of continuous states reduce to the energy eigenvalues and the radial wave functions of the bound states at the poles of the scattering amplitude.",

keywords = "Bound states, Continuous states, Ring-shaped potential, Scattering amplitudes",

author = "Chen, {Chang Yuan} and Dong, {Shi Hai}",

note = "Funding Information: This work was supported by the Natural Science Foundation of the Education Bureau of Jingsu Province of China and the Special Foundation of Yancheng Teachers College, China.",

year = "2005",

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TY - JOUR

T1 - Exactly complete solutions of the Coulomb potential plus a new ring-shaped potential

AU - Chen, Chang Yuan

AU - Dong, Shi Hai

N1 - Funding Information: This work was supported by the Natural Science Foundation of the Education Bureau of Jingsu Province of China and the Special Foundation of Yancheng Teachers College, China.

PY - 2005/2/21

Y1 - 2005/2/21

N2 - A new exactly solvable ring-shaped potential is proposed. The energy eigenvalues and eigenfunctions of the bound states for the Schrödinger equation with this potential are presented analytically. The exact solutions of the continuous states of this quantum system are also obtained. The calculation formula of phase shifts is derived. Analytical properties of the scattering amplitude are discussed. We find that the energy of the particle and the radial wave functions of continuous states reduce to the energy eigenvalues and the radial wave functions of the bound states at the poles of the scattering amplitude.

AB - A new exactly solvable ring-shaped potential is proposed. The energy eigenvalues and eigenfunctions of the bound states for the Schrödinger equation with this potential are presented analytically. The exact solutions of the continuous states of this quantum system are also obtained. The calculation formula of phase shifts is derived. Analytical properties of the scattering amplitude are discussed. We find that the energy of the particle and the radial wave functions of continuous states reduce to the energy eigenvalues and the radial wave functions of the bound states at the poles of the scattering amplitude.

KW - Bound states

KW - Continuous states

KW - Ring-shaped potential

KW - Scattering amplitudes

UR - http://www.scopus.com/inward/record.url?scp=12844269942&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2004.12.062

DO - 10.1016/j.physleta.2004.12.062

M3 - Artículo

SN - 0375-9601

VL - 335

SP - 374

EP - 382

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 5-6

ER -

Exactly complete solutions of the Coulomb potential plus a new ring-shaped potential

Abstract

Keywords

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