STUDIES IN PERTURBATION THEORY. XI. LOWER BOUNDS TO ENERGY EIGENVALUES, GROUND STATE AND EXCITED STATES,

Abstract

The bracketing theorem in the partitioning technique for solving the Schrodinger equation may be used in principle to determine upper and lower bounds to energy eigenvalues. Practical lower bounds of any accuracy desired may be evaluated by utilizing the properties of 'inner projections' on finite manifolds in the Hilbert space. The method is applied to the ground state and excited states of a Hamiltonian having a positive definite perturbation V. Even if inspiration is derived from the method of intermediate Hamiltonians, the final results are of bracketing type and independent of this approach. The method is numerically illustrated in some accompanying papers. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 15, 1965
Accession Number
AD0625364

Entities

People

  • Per-olav Lowdin

Organizations

  • Uppsala University

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Differential Equations
  • Eigenvalues
  • Equations
  • Ground State
  • Hilbert Space
  • Mathematical Analysis
  • Mathematics
  • Perturbation Theory
  • Perturbations
  • Schrodinger Equation
  • Theorems

Readers

  • Approximation Theory.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Molecular Photonics/Laser Physics

Technology Areas

  • Space