"Pointwise" versus basis representations for two-dimensional spherical dynamics

Abstract

We compare pointwise representations and nondirect product basis representations for treating quantum dynamics in 2D (θ, φ) spherical polar coordinates. As pointwise representations we have considered a modified discrete variable representation (DVR) and the collocation representation (CR). As basis representations we used spherical harmonics with 2D Gaussian numerical quadratures (FBR) and the spectral collocation representation (SCR). These representations were tested on a simple model potential V(θ, φ) and on a realistic ArH2O potential (at fixed R) and the results were compared. The energies obtained from the pointwise representations considered were substantially less accurate than those obtained from the basis representations for given matrix sizes. The basis representations, especially the FBR, appear to require the least computational effort and to be the most simple and accurate for quantum problems in spherical polar coordinates. This illustrates the difficulties in using pointwise representations for angular problems which do not have good direct product bases. © 1995 American Institute of Physics.