A GRID REPRESENTATION FOR SPHERICAL ANGLES - DECOUPLING OF THE ANGULAR-MOMENTUM OPERATOR

The angular momentum operator which is a function of the orientational angle theta and the azimuthal angle phi may be split into the phi-dep endent and phi-independent parts so that the split exponential operato r method can be exactly implemented (with orthogonal transformations) in a direct product discrete variable representation of theta and phi. Although one loses the exact representation of the angular momentum i n the spherical harmonic basis, the direct product representations hav e been proved to converge and to be stable and efficient. An advantage is that computational time for a wave-packet propagation (for a matri x-vector product) is reduced for split exponential propagators since a direct product representation is preserved for all the angles. (C) 19 97 American Institute of Physics. [S0021-9606(97)01644-9].