Table of Contents
ISRN Mathematical Physics
Volume 2012 (2012), Article ID 461452, 11 pages
http://dx.doi.org/10.5402/2012/461452
Research Article

Comparison Theorems for the Position-Dependent Mass Schrödinger Equation

Theoretical Physics Department, FFEKS, Dniepropetrovsk National University, 72 Gagarin Avenue, Dniepropetrovsk 49010, Ukraine

Received 13 August 2011; Accepted 13 September 2011

Academic Editor: E. Yomba

Copyright © 2012 D. A. Kulikov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The following comparison rules for the discrete spectrum of the position-dependent mass (PDM) Schrödinger equation are established. (i) If a constant mass 𝑚0 and a PDM 𝑚(x) are ordered everywhere, that is either, 𝑚0𝑚(x) or 𝑚0𝑚(x), then the corresponding eigenvalues of the constant-mass Hamiltonian and of the PDM Hamiltonian with the same potential and the BenDaniel-Duke ambiguity parameters are ordered. (ii) The corresponding eigenvalues of PDM Hamiltonians with the different sets of ambiguity parameters are ordered if 2(1/𝑚(x)) has a definite sign. We prove these statements by using the Hellmann-Feynman theorem and offer examples of their application.