Generalized Algebraic Bargmann - Darboux Transformations

Algebraic Bargmann and Darboux transformations for equations of a more general form than the Schr\"odinger ones with an additional functional dependence h(r) in the right-hand side of equations are constructed. The suggested generalized transformations turn into the Bargmann and Darboux transformations for both fixed and variable values of energy and an angular momentum.Comment: 6 pages, Late

Inverse problem and Darboux transformations for two-dimensional finite-difference Schredinger equation

A discrete version of the two-dimensional inverse scattering problem is considered. On this basis, algebraic transformations for the two-dimensional finite-difference Schredinger equation are elaborated.Comment: 12 pages, 1 figure (s_fig.eps), Late

Intertwining technique for a system of difference Schroedinger equations and new exactly solvable multichannel potentials

The intertwining operator technique is applied to difference Schroedinger equations with operator-valued coefficients. It is shown that these equations appear naturally when a discrete basis is used for solving a multichannel Schroedinger equation. New families of exactly solvable multichannel Hamiltonians are found