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

Symmetry

Axel Schulze-Halberg¹ 

[1] ¹Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, IN 46408, USA ²Escuela Superior de Cómputo, Instituto Politécnico Nacional, Col. Lindavista, 07738 México DF, Mexico

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

DOI  :  10.3390/sym1020115

来源: mdpi

【 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】

CC BY   
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.