@article {4181,
title = {Chain relations of reduced distribution functions and their associated correlation functions},
journal = {Journal of Chemical Physics},
volume = {108},
number = {2},
year = {1998},
note = {ISI Document Delivery No.: YP022Times Cited: 2Cited Reference Count: 33},
month = {Jan},
pages = {706-714},
type = {Article},
abstract = {For a closed system, the integration (trace in the quantum case) over one particle of a reduced distribution function is related to the reduced distribution function of one lower order, The particular details of this "chain" relation depend sensitively on the detailed manner in which the reduced distribution functions are defined, specifically their normalization. Correlation functions are defined in terms of reduced distribution functions, which fixes the normalization of the correlation functions and, provided they exist, their associated chain relations. Chain relations for the correlation functions are shown to exist for normalizations of generic type but not for normalizations of specific type. The normalization requirement is shown, in general, to prevent the direct association of correlation functions with physical clusters, which is commonly assumed in the literature, These relations are illustrated for an ideal gas of monomers and dimers. The effect of taking the thermodynamic limit on the chain relations for this system is discussed. This illustrates how the thermodynamic limit generally destroys the chain relations. (C) 1998 American Institute of Physics.},
keywords = {BOUND-STATES, DECAY, DIMER FORMATION, KINETIC-EQUATIONS, MECHANICS, QUANTUM},
isbn = {0021-9606},
url = {://000071233400037},
author = {Alavi, S. and Wei, G. W. and Snider, R. F.}
}
@article {3811,
title = {The quadrature discretization method (QDM) in the solution of the Schrodinger equation with nonclassical basis functions},
journal = {Journal of Chemical Physics},
volume = {104},
number = {11},
year = {1996},
note = {ISI Document Delivery No.: TY728Times Cited: 34Cited Reference Count: 66},
month = {Mar},
pages = {4137-4150},
type = {Article},
abstract = {A discretization method referred to as the Quadrature Discretization Method (QDM) is introduced for the solution of the Schrodinger equation. The method has been used previously for the solution of Fokker-Planck equations. The Fokker-Planck equation can be transformed to a Schrodinger equation with a potential of the form that occurs in supersymmetric quantum mechanics, For this class of potentials, the groundstate wave function is known. The QDM is based on the discretization of the wave function on a grid of points that coincide with the points of a quadrature. The quadrature is based on a set of nonclassical polynomials orthogonal with respect to a weight function determined by the potential function in the Schrodinger equation. For the Fokker-Planck operator, the weight function that provides rapid convergence of the eigenvalues are the steady distributions at infinite time, that is, the ground state wave functions. In the present paper, the weight functions used in an analogous solution of the Schrodinger equation are related to the ground state wave functions if known, or some approximate form. Calculations are carried out for a model systems, the Morse potential, and for the vibrational levels of O-2 and Ar-Xe with realistic pair potentials. For O-2, the wave functions are used to calculate the vibrationally inelastic transition amplitudes for a Morse potential and compared with exact analytic results. The eigenvalues of a two-dimensional Schrodinger equation with the Henon-Heiles potential are also calculated. The rate of convergence of the eigenvalues and the eigenfunctions of the Schrodinger equation is very rapid with this approach. (C) 1996 American Institute of Physics.},
keywords = {BOUND-STATES, COEFFICIENTS, DISCRETE-ORDINATE METHOD, EIGENVALUE PROBLEMS, FOKKER-PLANCK EQUATION, ORTHOGONAL POLYNOMIALS, POTENTIALS, QUANTUM-MECHANICS, RECURRENCE, ROVIBRATIONAL STATES},
isbn = {0021-9606},
url = {://A1996TY72800030},
author = {Shizgal, B. D. and Chen, H.}
}