Analytic Results in the Position-Dependent Mass Schrödinger Problem

  title={Analytic Results in the Position-Dependent Mass Schr{\"o}dinger Problem},
  author={M. S. Cunha and Hugo R. Christiansen},
  journal={Communications in Theoretical Physics},
  pages={642 - 650}
We investigate the Schrödinger 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 tanh2 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… 

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