New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach

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 Pöschl-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.

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

References in corpus (2)

• Nonlinear Supersymmetry for Spectral Design in Quantum Mechanics
• SUSY-Approach for Investigation of Two-Dimensional Quantum Mechanical Systems

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• Solution of Second Order Supersymmetrical Intertwining Relations in Minkowski Plane
• Coherent states of the two-dimensional non-separable supersymmetric Morse potential