Unified treatment of the bound states of the Schiöberg and the Eckart potentials using Feynman path integral approach

doi:10.1088/1674-1056/24/2/020302

›› 2015, Vol. 24 ›› Issue (2): 20302-020302.doi: 10.1088/1674-1056/24/2/020302

Unified treatment of the bound states of the Schiöberg and the Eckart potentials using Feynman path integral approach

A. Diaf

Laboratoire de l'Énergie et des Systèmes Intelligents, Université de Khemis Miliana, Route de Thénia, Khemis Miliana, 44225, Algérie

收稿日期:2014-06-09 修回日期:2014-09-10 出版日期:2015-02-05 发布日期:2015-02-05
基金资助:
Project supported by CNEPRU (Grant No. D03920130021).

Unified treatment of the bound states of the Schiöberg and the Eckart potentials using Feynman path integral approach

A. Diaf

Laboratoire de l'Énergie et des Systèmes Intelligents, Université de Khemis Miliana, Route de Thénia, Khemis Miliana, 44225, Algérie

Received:2014-06-09 Revised:2014-09-10 Online:2015-02-05 Published:2015-02-05
Contact: A. Diaf E-mail:s_ahmed_diaf@yahoo.fr
Supported by:
Project supported by CNEPRU (Grant No. D03920130021).

摘要/Abstract

摘要： We obtain analytical expressions for the energy eigenvalues of both the Schiöberg and Eckart potentials using an approximation of the centrifugal term. In order to determine the l-states solutions, we use the Feynman path integral approach to quantum mechanics. We show that by performing nonlinear space-time transformations in the radial path integral, we can derive a transformation formula that relates the original path integral to the Green function of a new quantum solvable system. The explicit expression of bound state energy is obtained and the associated eigenfunctions are given in terms of hypergeometric functions. We show that the Eckart potential can be derived from the Schiöberg potential. The obtained results are compared to those produced by other methods and are found to be consistent.

关键词: path integrals, l-states, Schiö, berg potential, Eckart potential

Abstract: We obtain analytical expressions for the energy eigenvalues of both the Schiöberg and Eckart potentials using an approximation of the centrifugal term. In order to determine the l-states solutions, we use the Feynman path integral approach to quantum mechanics. We show that by performing nonlinear space-time transformations in the radial path integral, we can derive a transformation formula that relates the original path integral to the Green function of a new quantum solvable system. The explicit expression of bound state energy is obtained and the associated eigenfunctions are given in terms of hypergeometric functions. We show that the Eckart potential can be derived from the Schiöberg potential. The obtained results are compared to those produced by other methods and are found to be consistent.

Key words: path integrals, l-states, Schiöberg potential, Eckart potential

中图分类号: (Formalism)

03.65.Ca

03.65.-w (Quantum mechanics) 03.65.Ge (Solutions of wave equations: bound states)

A. Diaf. Unified treatment of the bound states of the Schiöberg and the Eckart potentials using Feynman path integral approach[J]. , 2015, 24(2): 20302-020302.

A. Diaf. Unified treatment of the bound states of the Schiöberg and the Eckart potentials using Feynman path integral approach[J]. Chin. Phys. B, 2015, 24(2): 20302-020302.

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Unified treatment of the bound states of the Schiöberg and the Eckart potentials using Feynman path integral approach

Unified treatment of the bound states of the Schiöberg and the Eckart potentials using Feynman path integral approach

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