New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach
High Energy Physics - Theory
2009-11-10 v2 Mesoscale and Nanoscale Physics
Mathematical Physics
math.MP
Abstract
New solutions for second-order intertwining relations in two-dimensional SUSY QM are found via the repeated use of the first order supersymmetrical transformations with intermediate constant unitary rotation. Potentials obtained by this method - two-dimensional generalized P\"oschl-Teller potentials - appear to be shape-invariant. The recently proposed method of separation of variables is implemented to obtain a part of their spectra, including the ground state. Explicit expressions for energy eigenvalues and corresponding normalizable eigenfunctions are given in analytic form. Intertwining relations of higher orders are discussed.
Cite
@article{arxiv.hep-th/0409153,
title = {New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach},
author = {M. V. Ioffe and P. A. Valinevich},
journal= {arXiv preprint arXiv:hep-th/0409153},
year = {2009}
}
Comments
21 pages. Some typos corrected; imrovements added in Subsect.4.2; some references added