TIME-INDEPENDENT PERTURBATION THEORY BY GAUGE TRANSFORMATIONS,

Abstract

It is shown that a given solution of a one-electron Schrodinger equation for Hamiltonian (Ho) is also the solution to the Schrodinger equation for a particular gauge-transformed Hamiltonian when any given perturbation is added to Ho. This transformation is obtained from solutions to inhomogeneous partial differential equations similar to those of Dalgarno and Schwartz and it has the virtue of giving the energy expectation value in a particularly simple form. The corresponding many-electron gauge-transformation is also treated, and despite the fact that the equations obtained are in general not exactly soluble, the procedure does provide a useful visualization of the electron correlation contributions to the energy. An approximation for multi-center wave functions, which amounts to choosing a different gauge for each center, is also presented and the error introduced is discussed. (Author)

Document Details

Document Type
Technical Report
Publication Date
Apr 04, 1963
Accession Number
AD0416273

Entities

People

  • Jeremy I. Musher

Organizations

  • Harvard University

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Electrons
  • Equations
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Perturbation Theory
  • Perturbations
  • Real Variables
  • Schrodinger Equation
  • Wave Equations
  • Wave Functions

Fields of Study

  • Physics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Molecular Photonics/Laser Physics
  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.

Technology Areas

  • Microelectronics