A new exactly solvable two-dimensional quantum model not amenable to separation of variables

Abstract

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