$\hbar$-expansion for the Schr\"odinger equation with a position-dependent mass

D. A. Kulikov; V. M. Shapoval

$\hbar$-expansion for the Schr\"odinger equation with a position-dependent mass

Quantum Physics 2012-06-11 v1

Authors: D. A. Kulikov , V. M. Shapoval

Abstract

A recursion technique of obtaining the asymptotical expansions for the bound-state energy eigenvalues of the radial Schr\"odinger 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.

Keywords

position-dependent mass Schrödinger equation $\hbar$-expansion bound-state energy eigenvalues Coulomb potential asymptotic expansion

Cite

@article{arxiv.1206.1666,
  title  = {$\hbar$-expansion for the Schr\"odinger equation with a position-dependent mass},
  author = {D. A. Kulikov and V. M. Shapoval},
  journal= {arXiv preprint arXiv:1206.1666},
  year   = {2012}
}

Comments

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

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