Journal of Physical Studies 15(4), Article 4001 [6 pages] (2011)
DOI: https://doi.org/10.30970/jps.15.4001

ℏ-EXPANSION FOR THE SCHRÖDINGER EQUATION WITH A POSITION-DEPENDENT MASS

D. A. Kulikov¹, V. M. Shapoval²
¹Theoretical Physics Department, Oles Honchar Dnipropetrovsk National University,
72 Gagarin Avenue, Dnipropetrovsk, 49010, Ukraine, kulikov@dsu.dp.ua,
²Bogolyubov Institute for Theoretical Physics,
14-b Metrolohichna St., Kiev, 03680, Ukraine,
shapoval@bitp.kiev.ua

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.

PACS number(s): 03.65.-w, 03.65.Ge, 03.65.Sq