## Analytic results in the position-dependent mass Schrodinger problem    [PDF]

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\$
View original: http://arxiv.org/abs/1306.0933