Supersymmetry of Generalized Linear Schrödinger Equations in (1+1) Dimensions

Symmetry

关键词: time-dependent Schrödinger equation;    supersymmetry;    Darboux transformation;   

DOI  :  10.3390/sym1020115

来源: DOAJ

【 摘 要 】

We review recent results on how to extend the supersymmetry SUSY normalism in Quantum Mechanics to linear generalizations of the time-dependent Schrödinger equation in (1+1) dimensions. The class of equations we consider contains many known cases, such as the Schrödinger equation for position-dependent mass. By evaluating intertwining relations, we obtain explicit formulas for the interrelations between the supersymmetric partner potentials and their corresponding solutions. We review reality conditions for the partner potentials and show how our SUSY formalism can be extended to the Fokker-Planck and thenonhomogeneous Burgers equation.

【 授权许可】

Unknown