Abstract
A class of three-dimensional models which satisfy supersymmetric intertwining relations with the simplest - oscillator-like - variant of shape invariance is constructed. It is proved that the models are not amenable to conventional separation of variables for the complex potentials, but their spectra are real and equidistant (like for isotropic harmonic oscillator). The special case of such potential with quadratic interaction is solved completely. The Hamiltonian of the system is non-diagonalizable, and its wave functions and associated functions are built analytically. The symmetry properties of the model and degeneracy of energy levels are studied.
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