  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
$V(x)=V_0 \sinh^2(x)$.
