TRUNCATED REACTION OPERATORS

Abstract

The reaction operator formulation for the exact solution of the Schrodinger equation is used with a truncated basis set to obtain approximate solutions. The relationship between this trun cated reaction operator formalism and the Rayleigh-Ritz variational method is emphasized and shown explicitly. The truncated reaction operator and its matrix elements are discussed in general; computed and discussed for a simple ex ample, the helium atom, using a three membered basis set. It is shown that the reaction operator can be replaced by a function which we call the effective perturbation. This function has very fundamental significance and may lend itself to accurate empiricism. Expressions are given com paring the effective perturbation with the per turbation and approximations to this function for the helium atom are computed.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jun 18, 1963
Accession Number
AD0410315

Entities

People

  • Joseph O. Hirschfelder
  • Kenneth M. Sando
  • S. Osvaldo Goscinski
  • William J. Meath

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Atoms
  • Coefficients
  • Computational Chemistry
  • Computations
  • Eigenvalues
  • Eigenvectors
  • Elements
  • Equations
  • Government Procurement
  • Ground State
  • Mathematical Analysis
  • Perturbations
  • Physical Properties
  • Quantum Properties
  • Variational Methods
  • Wave Functions

Fields of Study

  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Organic Chemistry