Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Atomic and Molecular Physics

Exact solution of Klein-Gordon equation for generalized asymmetrical Hartmann potentials

Zhong Li

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

Under the condition of an equal mixing of vector and scalar potentials,we have solved exactly the Klein Gordon equation in an asymmetrical generalized Hartmann potential.With the boundary conditions of bound states,we have obtained the corresponding energy spectrum via an expression and wave functions in terms of hypergeometric functions.

Related papers

BOUND STATES OF KLEIN-GORDON EQUATION FOR HARTMANN SCALAR AND VECTOR POTENTIALS

Fa‐Lin Lu

By using the usual method of variable separation, bound states of Klein-Gordon equation with equal Hartmann scalar and vector potentials are solved. Properties of the system relate to three quantum numbers and parameters of Hartmann potential. The normalized angle wave function expressed in terms of the universal associated-Legendre polynomial and the normalized radial wave function expressed in terms of the confluent hypergeometric function are presented. The exacl energy spectrum equations are obtained. Bound states of Klein-Gordon equation for Hydrogen potential are special cases for the Hartmann potential in the Letter.

Journal of Anhui Normal University•Jan 1, 2005•0 citations

The relativistic scattering states of a spinless particle in the Hartmann potentials

Chang-Yuan Chen, Fa‐Lin Lu, Dong‐Sheng Sun

In this paper, exact solutions of scattering states of the Klein–Gordon equation with Hartmann potentials are studied under the conditions that the vector potential is equal to the scalar potential and that the vector potential is equal to the minus scalar potential. The normalized wave functions of scattering states on the ` k /2π scale' and the calculation formula of phase shifts are presented. Analytical properties of the scattering amplitude are discussed.

Physica Scripta•Jul 1, 2008•7 citations

Bound states of Klein-Gordon equation for ring-shaped harmonic oscillator scalar and vector potentials

Qiang Wen-Chao

Solving Klein-Gordon equation with equal ring-shaped harmonic oscillator scalar and vector potentials, we obtain the exact normalized bound-state wavefunction and energy equation.

Chinese Physics•Jan 20, 2003•43 citations

Bound states of the Klein–Gordon equation for ring-shaped Kratzer-type potential

Qiang Wen Chao

The exact normalized bound state wavefunctions and energy equations of Klein–Gordon equation with equal scalar and vector ring-shaped Kratzer-type potential have been obtained.

Chinese Physics•Apr 29, 2004•43 citations

Bound state solutions of D-dimensional Klein–Gordon equation with hyperbolic potential

C. A. Onate, A. N. Ikot, M. C. Onyeaju +1 more

By using the basic supersymmetric quantum mechanics concepts and formalism, the energy eigenvalue equation and the corresponding wave function of the Klein–Gordon equation with vector and scalar potentials for an arbitrary dimensions are obtained together with hyperbolic potential using a suitable approximation scheme to the orbital centrifugal term. The non-relativistic limit is obtained and the numerical values for various values of D, n, α and ℓ are obtained.

Karbala International Journal of Modern Science•Dec 27, 2016•20 citations

Bound states of Klein-Gordon equation for ring-shaped non-spherical harmonic oscillator potentials

Fa‐Lin Lu, Chen Chang-Yuan, 盐城师范学院物理系，盐城 224002

By using the ordinary method of variable separation,the bound states of Klein-Gordon equation of the ring-shaped non-spherical harmonic oscillator with equal scalar and vector potentials are solved. The normalized angular wave function expressed in terms of the universal associatedLegendre polynomial and the normalized radial wave function expressed in terms of the confluent hyper-geometric function are presented. The exact energy spectrum equations are obtained.

Acta Physica Sinica•Jan 1, 2004•4 citations
Under the condition of an equal mixing of vector and scalar potentials,we have solved exactly the Klein Gordon equation in an asymmetrical generalized Hartmann potential.With the boundary conditions of bound states,we have obtained the corresponding energy spectrum via an expression and wave functions in terms of hypergeometric functions.
By using the usual method of variable separation, bound states of Klein-Gordon equation with equal Hartmann scalar and vector potentials are solved. Properties of the system relate to three quantum numbers and parameters of Hartmann potential. The normalized angle wave function expressed in terms of the universal associated-Legendre polynomial and the normalized radial wave function expressed in terms of the confluent hypergeometric function are presented. The exacl energy spectrum equations are obtained. Bound states of Klein-Gordon equation for Hydrogen potential are special cases for the Hartmann potential in the Letter.