The solutions of the quantum mechanical wave equations for singular potentials are re-examined. It is shown that a set of orthonormal wave functions with complex energy eigenvalues (E n = W n ±iiV n ) is obtained if certain natural analyticity requirements are imposed on the form of the potentials. In general, the result is interpreted in the following way: W n is the most probable position of the energy level for various types of cutoff and T n is a measure of the probable error.