New Exactly Solvable Two-Dimensional Quantum Model Not Amenable to Separation of Variables

Details New Exactly Solvable Two-Dimensional Quantum Model Not Amenable to Separation of Variables New Exactly Solvable Two-Dimensional Quantum Model Not Amenable to Separation of Variables

2010-10-11

arxiv.org/abs/1010.2119v1

J.Phys.A43:485303,2010

Physics

High Energy Physics

High Energy Physics - Theory

23 pages

Scientific paper

10.1088/1751-8113/43/48/485303

The supersymmetric intertwining relations with second order supercharges allow to investigate new two-dimensional model which is not amenable to standard separation of variables. The corresponding potential being the two-dimensional generalization of well known one-dimensional P\"oschl-Teller model is proven to be exactly solvable for arbitrary integer value of parameter $p:$ all its bound state energy eigenvalues are found analytically, and the algorithm for analytical calculation of all wave functions is given. The shape invariance of the model and its integrability are of essential importance to obtain these results.

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