New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach

Details New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach

2004-09-15

arxiv.org/abs/hep-th/0409153v2

J.Phys. A38 (2005) 2497-2510

Physics

High Energy Physics

High Energy Physics - Theory

21 pages. Some typos corrected; imrovements added in Subsect.4.2; some references added

Scientific paper

10.1088/0305-4470/38/11/011

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 $SUSY-$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.

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