Analytical solution of two-dimensional Scarf II model by means of SUSY methods

A new two-dimensional quantum model—a generalization of Scarf II—is completely solved analytically for integer values of the parameter. This model not being amenable to the conventional procedure of separation of variables is solved by a recently proposed method of supersymmetrical separation. The latter is based on two constituents of SUSY Quantum Mechanics: the intertwining relations with second order supercharges and the property of shape invariance. As a result, all energies of bound states were found, and the analytical expressions for corresponding wave functions were obtained. - Highlights: ► 2-dim quantum Scarf II model is solved completely for specific values of parameter. ► Hierarchy of models for integer values of parameters is solved by shape invariance. ► All bound state wave functions are expressed in terms of Jacobi polynomials.