Exact solution to the time-dependent Schrödinger equation in two dimensions

With a view to obtaining an exact analytic solution to the time-dependent Schrödinger wave equation for noncentral harmonic and anharmonic potentials in two dimensions, we make use of an ansatz for the eigenfunction in conjunction with the methods of Burgan et al. [Phys. Lett. 74A, 11 (1979)] and Ray [Phys. Rev. A 26, 729 (1982)]. While the method is found to work well for a restricted class of harmonic potentials, its limitations in the case of anharmonic potentials are pointed out.