Journal of Mathematical Physics
Darboux transformations in one variable form the basis for the factorization methods and have numerous applications to geometry, nonlinear equations and SUSY quantum mechanics. In spite of this wide range of applications the theory of Darboux transformations in two variables and its elegant relationship to analytic complex functions has not been recognized in the literature. To close this gap we develop in this paper the theory of Darboux transformation in the context of Schrodinger equations in two variables. This yields a constructive algorithm to determine the relationship between potential functions which are related by Darboux transformations.
Copyright 2005 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Mathematical Physics 46(8) and may be found at http://link.aip.org/link/doi/10.1063/1.2000727.
Humi, M. (2005). Darboux Transformations for Schrodinger Equations in Two Variables. Journal of Mathematical Physics, 46(8) http://dx.doi.org/10.1063/1.2000727