Analytic Results in the Position-Dependent Mass Schrodinger Problem

作者：Cunha M S^*; Christiansen H R

来源：Communications in Theoretical Physics, 2013, 60(6): 642-650.

• Schrodinger equation
• position-dependent mass
• Heun equation

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.

• 出版日期2013-12