New method for solving multidimensional scattering problem
type: Item
instance of: scholarly article
title: New method for solving multidimensional scattering problem
zbMATH Open document ID: 0714.65094
DOI: 10.1016/0021-9991(91)90292-S
published in: Journal of Computational Physics
publication date: 1991-01-01T00:00:00Z
review text: The quantum mechanical problem of scattering of a particle with internal structure is studied. A new method is proposed without expanding the wave function over some basis and without calculating matrix elements of the Hamiltonian. For some variables \(\Omega\) characterizing the scatterer a difference net \(\Omega_ i\) is introduced, the distance between the nodes is characterized by the integration step h. These variables are discrete. One variable R (the distance from the particle to the center of mass of the scatterer) is continuous. The multidimensional Schrödinger equation is approximated by a system of differential-difference equations for the vector \(\psi\) (R,\(\Omega\)). The scattering problem is formulated by the procedure of the author [J. Comput. Phys. 65, 1-17 (1986; Zbl 0588.65064)] as a system of nonlinear functional equations the solution of which is equivalent to the determination of the wave function. As an example the ground state energies of the hydrogen atom in a homogeneous magnetic field are calculated. Scattering of a neutral particle on a di-atomic molecule is mentioned as another example.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 81U20
zbMATH DE Number: 4176399
zbMATH Keywords: scattering
zbMATH Keywords: wave function
zbMATH Keywords: difference net
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: differential-difference equations
zbMATH Keywords: hydrogen atom
author: V. S. Melezhik
MaRDI profile type: Publication
cites work: Continuous analog of Newton method in the multichannel scattering problem
cites work: Q5732047
cites work: Q3312699
cites work: Numerical solution of a system of integrodifferential equations arising from the quantum mechanical three-body problem with Coulomb interaction
cites work: A new look at the Lanczos algorithm for solving symmetric systems of linear equations
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full work available at URL: 0021-9991(91)90292-s
OpenAlex ID: W2011036012
description: scientific article; zbMATH DE number 4176399