A grid representation for spherical angles: Decoupling of the angular momentum operator

Abstract

The angular momentum operator which is a function of the orientational angle θ and the azimuthal angle φ may be split into the φ-dependent and φ-independent parts so that the split exponential operator method can be exactly implemented (with orthogonal transformations) in a direct product discrete variable representation of θ and φ. Although one loses the exact representation of the angular momentum in the spherical harmonic basis, the direct product representations have been proved to converge and to be stable and efficient. An advantage is that computational time for a wave-packet propagation (for a matrix-vector product) is reduced for split exponential propagators since a direct product representation is preserved for all the angles.