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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
Abstract: 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
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Schulze-Halberg, A.; Carballo Jimenez, J.M. Supersymmetry of Generalized Linear Schrödinger Equations in (1+1) Dimensions. Symmetry 2009, 1, 115-144.
Schulze-Halberg A, Carballo Jimenez JM. Supersymmetry of Generalized Linear Schrödinger Equations in (1+1) Dimensions. Symmetry. 2009; 1(2):115-144.
Schulze-Halberg, Axel; Carballo Jimenez, Juan M. 2009. "Supersymmetry of Generalized Linear Schrödinger Equations in (1+1) Dimensions." Symmetry 1, no. 2: 115-144.