New Two-Dimensional Integrable Quantum Models from SUSY Intertwining

Abstract

Supersymmetrical intertwining relations of second order in the derivatives are investigated for the case of supercharges with deformed hyperbolic metric $g_{ik}=diag(1,-a^2)$. Several classes of particular solutions of these relations are found. The corresponding Hamiltonians do not allow the conventional separation of variables, but they commute with symmetry operators of fourth order in momenta. For some of these models the specific SUSY procedure of separation of variables is applied.

18 pages

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• Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics
• Pseudo-Hermiticity of an Exactly Solvable Two-Dimensional Model
• New Exactly Solvable Two-Dimensional Quantum Model Not Amenable to Separation of Variables
• Analytical Solution of Two-Dimensional Scarf II Model by Means of SUSY Methods
• Three-Dimensional Solutions of Supersymmetrical Intertwining Relations and Pairs of Isospectral Hamiltonians
• Supersymmetric Partners of the One-Dimensional Infinite Square Well Hamiltonian
• Solution of Second Order Supersymmetrical Intertwining Relations in Minkowski Plane