The Laguerre pseudospectral method for the two-dimensional Schrodinger equation with symmetric nonseparable potentials

The Hermite pseudospectral method is one of the natural techniques for the numerical treatment of the problems defined over unbounded domains such as two-dimensional time-independent Schrodinger equation on the whole real plane. However, it is shown here that for the symmetric potentials, transformation of the problem over the first quadrant and the application of the Laguerre pseudospectral method reduce the cost by a factor of four when compared to the Hermite pseudospectral method.