LOWER BOUNDS FOR EIGENVALUES

Abstract

Various methods for the calculation of lower bounds for eigenvalues are examined, including those of Weinstein, Temple, Bazley and Fox, Gay, and Miller. It is shown how all of these can be derived in a unified manner by the projection technique. The alternate forms obtained for the Gay formula show how a considerably improved method can be readily obtained. Applied to the ground state of the helium atom with a simple screened hydrogenic trial function, this new method gives a lower bound closer to the true energy than the best upper bound obtained with this form of trial function. Possible routes to further improved methods are suggested.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1965
Accession Number
AD0464263

Entities

People

  • E. B. Wilson Jr.

Organizations

  • Harvard University

Tags

Communities of Interest

  • Advanced Electronics

DTIC Thesaurus Topics

  • Classification
  • Contractors
  • Contracts
  • Eigenvalues
  • Eigenvectors
  • Energy Levels
  • Equations
  • Government Procurement
  • Governments
  • Ground State
  • Military Research
  • Perturbation Theory
  • Quantum Mechanics
  • Security
  • Universities

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra
  • Powder metallurgy of Titanium alloys.