The linear algebraic method for electron-molecule collisions

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In order to find numerical solutions to many problems in physics, chemistry and engineering it is necessary to place the equations of motion (classical or quantal) of the variables of dynamical interest on a discrete mesh. The formulation of scattering theory in quantum mechanics is no exception and leads to partial differential or integral equations which may only be solved on digital computers. Typical approaches introduce a numerical grid or basis set expansion of the scattering wavefunction in order to reduce `the problem to the solution of a set of algebraic equations. Often it is more convenient to deal with ... continued below

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15 p.

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Collins, L. A. & Schneider, B. I. September 1995.

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  • Collins, L. A. Los Alamos National Lab., NM (United States)
  • Schneider, B. I. National Science Foundation, Arlington, VA (United States). Physics Div.

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Description

In order to find numerical solutions to many problems in physics, chemistry and engineering it is necessary to place the equations of motion (classical or quantal) of the variables of dynamical interest on a discrete mesh. The formulation of scattering theory in quantum mechanics is no exception and leads to partial differential or integral equations which may only be solved on digital computers. Typical approaches introduce a numerical grid or basis set expansion of the scattering wavefunction in order to reduce `the problem to the solution of a set of algebraic equations. Often it is more convenient to deal with the scattering matrix or phase amplitude rather than the wavefunction but the essential features of the numerics are unchanged. In this section we will formulate the Linear Algebraic Method (LAM) for electron-atom/molecule scattering for a simple, one-dimensional radial potential. This will illustrate the basic approach and enable the uninitiated reader to follow the subsequent discussion of the general, multi-channel, electron-molecule formulation without undue difficulty. We begin by writing the Schroedinger equation for the s-wave scattering of a structureless particle by a short-range, local potential.

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15 p.

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OSTI as DE95016931

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  • comparative study of current methodologies in electron-molecule scattering, Cambridge, MA (United States), 11-13 Mar 1995

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  • Other: DE95016931
  • Report No.: LA-UR--95-2878
  • Report No.: CONF-9503177--1
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 105883
  • Archival Resource Key: ark:/67531/metadc621982

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • September 1995

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  • June 16, 2015, 7:43 a.m.

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  • Feb. 29, 2016, 3:55 p.m.

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Collins, L. A. & Schneider, B. I. The linear algebraic method for electron-molecule collisions, article, September 1995; New Mexico. (digital.library.unt.edu/ark:/67531/metadc621982/: accessed April 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.