New two-dimensional quantum models partially solvable by the supersymmetrical approach

New solutions for second-order intertwining relations in two-dimensional SUSY QM are found via repeated use of the first-order supersymmetrical transformations with intermediate constant unitary rotation. Potentials obtained by this method—two-dimensional generalized Poschl–Teller potentials—appear to be shape-invariant. The recently proposed method of SUSY—separation of variables—is implemented to obtain a part of their spectra, including the ground state. Explicit expressions for energy eigenvalues and corresponding normalizable eigenfunctions are given in an analytic form. Intertwining relations of higher orders are discussed.