ℏ-expansion for the Schrödinger equation with a position-dependent mass

2012/06/08 by D. A. Kulikov, Kulikov, D. A., V. M. Shapoval +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics #quant-ph

paper · pdf · doi:10.48550/arxiv.1206.1666

10 pages, translated version of a paper: D.A. Kulikov, V.M. Shapoval, J.Phys.Stud. 15 (2011) 4001

arxiv created 2012/06/08 · openalex publication_date 2012/06/08 · arxiv updated 2012/06/11 · openalex created_date 2018/06/21 · openalex updated_date 2026/07/28

Abstract

A recursion technique of obtaining the asymptotical expansions for the bound-state energy eigenvalues of the radial Schrödinger equation with a position-dependent mass is presented. As an example of the application we calculate the energy eigenvalues for the Coulomb potential in the presence of position-dependent mass and we derive the inequalities regulating the shifts of the energy levels from their constant-mass positions.

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