Supersymmetry of time-dependent Schrödinger equations with effective mass

Abstract

Abstract:We establish the supersymmetry formalism for time-dependent Schrödinger equations with effective mass and show that the corresponding supersymmetric transformations are equivalent to effective mass Darboux transformations.

Reduction of Time‐Dependent Schrödinger Equations with Effective Mass to Stationary Schrödinger Equations

“…In the stationary case, particular potentials with effective mass have been studied mainly by means of point canonical transformations [5][6][7] and Darboux transformations (resp., supersymmetric factorization) [8][9][10]. Recently, these methods have also been elaborated for the fully timedependent case [11][12][13]. However, the main problem of accessing time-dependent Schrödinger equations (TDSE) with effective mass is the lack of known solvable cases.…”