A A Suzko and A Schulze-Halberg 2009 J. Phys. A: Math. Theor. 42 295203 doi:10.1088/1751-8113/42/29/295203
Darboux transformations and supersymmetry for the generalized Schrödinger equations in (1+1) dimensions
A A Suzko1,2 and A Schulze-Halberg3
Show affiliationsWe study intertwining relations, supersymmetry and Darboux transformations for generalized Schrödinger equations in (1+1) dimensions. We obtain intertwiners in an explicit form by means of which we construct arbitrary-order Darboux transformations for our class of equations. We develop a corresponding supersymmetric formulation and prove equivalence of the Darboux transformations with the supersymmetry formalism. Finally, we show that our Darboux transformations can also be constructed by means of point transformations, avoiding the use of intertwiners.
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Issue 29 (24 July 2009)
Received 14 April 2009, in final form 11 June 2009
Published 30 June 2009
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Darboux transformations and supersymmetry for the generalized Schrödinger equations in (1+1) dimensions
A A Suzko and A Schulze-Halberg 2009 J. Phys. A: Math. Theor. 42 295203
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