Solvable PT-symmetric potentials in higher dimensions

PT-symmetric, non-relativistic quantum mechanical potentials are discussed in two and three spatial dimensions. Conditions are formulated under which these potentials are PT-symmetric and can be solved exactly by the separation of the radial and angular variables. It is found that the angular variables play an essential role in introducing non-Hermiticity via the imaginary potential terms. A simple partially exactly solvable potential is used to demonstrate various aspects of PT symmetry in both two and three dimensions. Possible generalizations of the results are outlined.