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Communications in Theoretical Physics

Exact Solutions to Three-Dimensional Schrödinger Equation with an Exponentially Position-Dependent Mass

Cai Chang-Ying, Zhongzhou Ren, Ju Guo-Xing

Published Jun 1, 2005• 24 citations
Publisher

Abstract

For an exponentially position-dependent mass, we obtain the exact solutions of the three-dimensional Schrödinger equation by using coordinate transformation method for the reference problems with Coulomb potential, Kratzer potential, and spherically square potential well of infinite depth, respectively. The explicit expressions for the energy eigenvalues and the corresponding eigenfunctions of the three systems are presented.

DOI
10.1088/0253-6102/43/6/011

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For an exponentially position-dependent mass, we obtain the exact solutions of the three-dimensional Schrödinger equation by using coordinate transformation method for the reference problems with Coulomb potential, Kratzer potential, and spherically square potential well of infinite depth, respectively. The explicit expressions for the energy eigenvalues and the corresponding eigenfunctions of the three systems are presented.
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For an effective mass distribution that is an exponential function of the radial coordinate, the analytical solutions of the three-dimensional Schrdinger equ ation are obtained by using the coordinate transformation method for the referen ce problems with Coulomb potential, Kratzer potential and spherically square pot ential well of infinite depth, respectively. The explicit analytical expressions for the energy eigenvalues and the corresponding eigenfunctions of the three sy stems are presented.
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