THE GENERALIZED DISCRETE VARIABLE REPRESENTATION - AN OPTIMAL-DESIGN

The generalized discrete variable representation, as opposed to the di screte variable representation, of a Hamiltonian is such that it can g ive accurate eigenvalues of the Hamiltonian even if non-Gaussian quadr ature points and weights are used in its construction. A new method of building up the generalized discrete variable representation of a Ham iltonian has been described and its properties have been analyzed. Thi s new method appears to be optimal, meaning that no other design based on the same points, weights, and basis functions can. be conceived wh ich would give more accurate eigenvalues. Numerical calculations have revealed that, remarkable accuracy can be achieved even with general, non-Gaussian quadrature points and weights. (C) 1996 American Institut e of Physics.