M. S. Cunha, H. R. Christiansen
We investigate the Schrodinger equation for a particle with a nonuniform solitonic mass density. First, we discuss in extent the (nontrivial) $V(x)=0$ case whose solutions are hipergeometric 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 $V(x)=V_0 \sinh^2x$
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http://arxiv.org/abs/1306.0933
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