Discrete analogs of spherical harmonics and their use in quantum mechanics: The hyperquantization algorithm

Summary An algorithm for the solution of the Schrödinger equation in a discrete basis is illustrated with reference to the problem of quantization on spheres of any dimension (hyperquantization). It exploits the explicit construction of discrete analogs of spherical harmonics and leads to sparse matrix representations of the kinetic energy operator and a diagonal representation of the interaction potential. Applications are discussed for inelastic and reactive scattering.