Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics

Details Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics

2010-09-24

arxiv.org/abs/1009.4764v1

SIGMA 6:075,2010

Physics

Mathematical Physics

Scientific paper

10.3842/SIGMA.2010.075

Two different approaches are formulated to analyze two-dimensional quantum models which are not amenable to standard separation of variables. Both methods are essentially based on supersymmetrical second order intertwining relations and shape invariance - two main ingredients of the supersymmetrical quantum mechanics. The first method explores the opportunity to separate variables in the supercharge, and it allows to find a part of spectrum of the Schr\"odinger Hamiltonian. The second method works when the standard separation of variables procedure can be applied for one of the partner Hamiltonians. Then the spectrum and wave functions of the second partner can be found. Both methods are illustrated by the example of two-dimensional generalization of Morse potential for different values of parameters.

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