@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 {2781,
	title = {TIME-DEPENDENT NUCLEATION .2. A SEMICLASSICAL APPROACH},
	journal = {Journal of Chemical Physics},
	volume = {98},
	number = {7},
	year = {1993},
	note = {ISI Document Delivery No.: KV997Times Cited: 13Cited Reference Count: 20},
	month = {Apr},
	pages = {5713-5719},
	type = {Article},
	abstract = {The continuum approximation of the Becker-Doring birth and death equations [B. Shizgal and J. C. Barrett, J. Chem. Phys. 91, 6505 (1989)] leads to a Fokker-Planck equation for the continuous cluster distribution. This linear Fokker-Planck equation is solved with the expansion of the cluster distribution function in the eigenfunctions of the Fokker-Planck operator. The Fokker-Planck eigenvalue problem can be transformed into an equivalent Schrodinger equation. In this paper, the semiclassical Wentzel-Kramers-Brillouin (WKB) method and the corresponding supersymmetric WKB method are employed in the determination of the eigenvalues and eigenfunctions of the equivalent Schrodinger equation. We compare the approximate results with those obtained with a standard discretization scheme. We obtain eigenvalues and eigenfunctions of the Fokker-Planck operator which are in good agreement with the exact ones. The nucleation fluxes and associated time lags are also considered.},
	keywords = {ELECTRON THERMALIZATION, FOKKER-PLANCK EQUATIONS, WKB},
	isbn = {0021-9606},
	url = {<Go to ISI>://A1993KV99700055},
	author = {Demeio, L. and Shizgal, B.}
}
