We investigate the Schr6dinger 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 hypergeometri...We investigate the Schr6dinger 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 eigenstat, es for a potential of the form V （x） = Vo sinh2 z.展开更多
文摘We investigate the Schr6dinger 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 eigenstat, es for a potential of the form V （x） = Vo sinh2 z.
