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arXiv · 1306.0933

Analytic results in the position-dependent mass Schrodinger problem

M. S. Cunha·H. R. Christiansen
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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 $V(x)=V_0 \sinh^2(x)$.

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M. S. Cunha, H. R. Christiansen. 2013-11-30. Analytic results in the position-dependent mass Schrodinger problem. https://doi.org/10.1088/0253-6102%2F60%2F6%2F02

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