The fast Hankel transform as a tool in the solution of the time dependent Schrödinger equation

A new method is presented for the solution of the time dependent Schrödinger equation, expressed in polar or spherical coordinates. The radial part of the Laplacian operator is computed using a Fast Hankel Transform. An algorithm for the FHT is described, based on the Fast Fourier Transform. The accuracy of the Hankel method is checked for the two- and three-dimensional harmonic oscillator by comparing with the analytical solution. The Hankel method is applied to the system H + H₂ with Delves hyperspherical coordinates and is compared to the Fourier method.