NUMERICAL-SOLUTION OF THE TIME-DEPENDENT SCHRODINGER-EQUATION IN SPHERICAL COORDINATES BY FOURIER-TRANSFORM METHODS

We present a numerical Fourier-transform method for solving the time-dependent Schrodinger equation in spherical coordinates. The time propagation is accomplished with a novel implementation of a Crank-Nicholson scheme combined with a Feit-Fleck split-operator method. Calculations on model problems give results that are in excellent agreement with those obtained by other methods. The procedure avoids the numerical instabilities associated with the division by the sine of the polar angle. The propagator is unitary, does not require the calculation of any matrix elements, and uses no matrix multiplications other than fast Fourier transforms.