Analytic results in the position-dependent mass Schrodinger problem

Abstract

We investigate the Schrodinger equation for a particle with a nonuniform solitonic mass density. First, we discuss in extent the (nontrivial) position-dependent mass $V(x)=0$ case whose solutions are hypergeometric functions in ${\tanh }^2(x)$. Then, we consider an external hyperbolic-tangent potential. We show that the effective quantum mechanical problem is given by a Heun class equation and find analytically an eigenbasis for the space of solutions. We also compute the eigenstates for a potential of the form $V(x)=V_0{\sinh }^2(x)$.

Some typos corrected. Version to appear in Comm. Theor. Phys. (2013)

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