Next Article in Journal / Special Issue
On the Symmetry of a Zig-Zag and an Armchair Polyhex Carbon Nanotorus
Previous Article in Journal / Special Issue
The Relationship Between Morphological Symmetry and Immune Response in Wild-Caught Adult Bush-Crickets
Article Menu

Article Versions

Export Article

Open AccessReview
Symmetry 2009, 1(2), 115-144; doi:10.3390/sym1020115

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

Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, IN 46408, USA
Escuela Superior de Cómputo, Instituto Politécnico Nacional, Col. Lindavista, 07738 México DF, Mexico
Author to whom correspondence should be addressed.
Received: 3 September 2009 / Accepted: 2 October 2009 / Published: 6 October 2009
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
Download PDF [266 KB, uploaded 6 October 2009]


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.
Keywords: time-dependent Schrödinger equation; supersymmetry; Darboux transformation time-dependent Schrödinger equation; supersymmetry; Darboux transformation
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Schulze-Halberg, A.; Carballo Jimenez, J.M. Supersymmetry of Generalized Linear Schrödinger Equations in (1+1) Dimensions. Symmetry 2009, 1, 115-144.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top