An adaptable discrete variable representation based on coherent states

A novel approach for constructing a discrete variable representation (DVR) is described. The procedure involves two basis transformations. A finite, nonorthogonal, and overcomplete coherent state (CS) basis is transformed to an orthonormal basis via singular value decomposition (SVD). This orthonormal basis is then transformed to a DVR in the usual manner. This DVR is easily optimized for specific problems by restricting CS to relevant phase space regions. The SVD allows one to tailor the desired level of accuracy uniformly over the entire desired energy range. The method is illustrated with application to a two-dimensional Henon–Heiles potential.