@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 {7046,
	title = {RELAXATION OF HOT-ELECTRON DISTRIBUTIONS IN GAAS},
	journal = {Physical Review B},
	volume = {44},
	number = {7},
	year = {1991},
	note = {ISI Document Delivery No.: GC066Times Cited: 5Cited Reference Count: 42},
	month = {Aug},
	pages = {2969-2978},
	type = {Article},
	abstract = {The field-free equilibration of optically excited nonequilibrium hot electrons is studied theoretically with use of the Boltzmann kinetic equation. The analysis is limited to the situation where the longitudinal-optical-phonon scattering mechanism is dominant. The relaxation of the electron-energy-distribution function and of the average electron energy are investigated numerically for pulsed initial conditions with account taken of the exact collision integral within a single-parabolic-band model. It is shown that the energy dependence of the relevant scattering rate plays an important role in determining the relaxation of the hot-electron distribution.},
	keywords = {BOLTZMANN COLLISION OPERATOR, ENERGY RELAXATION, MONTE-CARLO METHOD, PHOTO-EXCITATION, PHOTOEXCITED CARRIERS, PROBLEM, QUANTUM WELLS, RUNAWAY, SEMICONDUCTORS, TRANSPORT, VARYING DRAG},
	isbn = {0163-1829},
	url = {<Go to ISI>://A1991GC06600013},
	author = {Kim, C. S. and Shizgal, B.}
}
