@article {1468,
	title = {Spectral convergence of the quadrature discretization method in the solution of the Schrodinger and Fokker-Planck equations: Comparison with sinc methods},
	journal = {Journal of Chemical Physics},
	volume = {125},
	number = {19},
	year = {2006},
	note = {ISI Document Delivery No.: 107OVTimes Cited: 3Cited Reference Count: 76Lo, Joseph Shizgal, Bernie D.},
	month = {Nov},
	pages = {17},
	type = {Article},
	abstract = {Spectral methods based on nonclassical polynomials and Fourier basis functions or sinc interpolation techniques are compared for several eigenvalue problems for the Fokker-Planck and Schrodinger equations. A very rapid spectral convergence of the eigenvalues versus the number of quadrature points is obtained with the quadrature discretization method (QDM) and the appropriate choice of the weight function. The QDM is a pseudospectral method and the rate of convergence is compared with the sinc method reported by Wei [J. Chem. Phys., 110, 8930 (1999)]. In general, sinc methods based on Fourier basis functions with a uniform grid provide a much slower convergence. The paper considers Fokker-Planck equations (and analogous Schrodinger equations) for the thermalization of electrons in atomic moderators and for a quartic potential employed to model chemical reactions. The solution of the Schrodinger equation for the vibrational states of I-2 with a Morse potential is also considered. (c) 2006 American Institute of Physics.},
	keywords = {BOLTZMANN COLLISION OPERATOR, DISCRETE-VARIABLE REPRESENTATIONS, EIGENVALUE PROBLEMS, ELECTRON THERMALIZATION, LANCZOS METHOD, MATRIX-ELEMENTS, NONCLASSICAL ORTHOGONAL POLYNOMIALS, ORDINATE METHOD, SINGULAR CONVOLUTION, SUPERSYMMETRIC QUANTUM-MECHANICS},
	isbn = {0021-9606},
	url = {<Go to ISI>://000242181800010},
	author = {Lo, J. and Shizgal, B. D.}
}
@article {4130,
	title = {The quadrature discretization method (QDM) in the calculation of the rotational-vibrational transitions in rare gas dimers},
	journal = {Theochem-Journal of Molecular Structure},
	volume = {391},
	number = {1-2},
	year = {1997},
	note = {ISI Document Delivery No.: WU757Times Cited: 3Cited Reference Count: 38},
	month = {Feb},
	pages = {131-139},
	type = {Article},
	abstract = {A discretization method referred to as the Quadrature Discretization Method (QDM) is employed for the determination of the rotational-vibrational states of the inert gas dimers. 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 non-classical polynomials orthogonal with respect to a weight function determined by the potential function in the Schroedinger equation. In this paper, the weight functions used in the solution of the Schroedinger equation are related to the ground state wavefunctions of the Morse potential that approximates the potential of interest. Calculations are carried out for vibrational energy levels for HF modelled with a Morse potential. Excellent agreement is obtained with the known spectrum of the Morse potential. The rate of convergence of the eigenvalues and the eigenfunctions of the Schroedinger equation is very rapid with this approach. The vibrational and rotational transitions for the rare gas dimers are calculated and compared with the results reported recently by Ogilvie and Wang (J. Mol. Struc., 291 (1993) 313). (C) 1997 Elsevier Science B.V.},
	keywords = {AR-XE, COEFFICIENTS, DISCRETE-VARIABLE REPRESENTATION, NE-KR, ORDINATE METHOD, POTENTIALS, quadrature discretion method, QUANTUM-MECHANICS, rare gas dimer, rotation-vibration, SCHRODINGER-EQUATION, Schroedinger equation, SPECTRA, STATES, TRANSITION},
	isbn = {0166-1280},
	url = {<Go to ISI>://A1997WU75700014},
	author = {Shizgal, B. D.}
}
