Higher Order Matrix SUSY Transformations in Two-Dimensional Quantum Mechanics
F. Cannata, M.V. Ioffe, A.I.Neelov, D.N. Nishnianidze
TL;DR
This paper develops a method for applying higher order supersymmetric transformations to two-dimensional quantum systems using matrix factorizations, exploring different iteration types and providing explicit examples.
Contribution
It introduces a matrix-based iteration procedure for SUSY transformations in 2D quantum mechanics, including the diagonal Hamiltonian case and explicit solution examples.
Findings
Successful implementation of matrix SUSY transformations in 2D
Demonstration of solution existence for diagonal Hamiltonians
Explicit examples illustrating the transformation process
Abstract
The iteration procedure of supersymmetric transformations for the two-dimensional Schroedinger operator is implemented by means of the matrix form of factorization in terms of matrix 2x2 supercharges. Two different types of iterations are investigated in detail. The particular case of diagonal initial Hamiltonian is considered, and the existence of solutions is demonstrated. Explicit examples illustrate the construction.
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