Accession Number:

AD0628315

Title:

THE CALCULATION OF UPPER AND LOWER BOUNDS OF ENERGY EIGENVALUES IN PERTURBATION THEORY BY MEANS OF PARTITIONING TECHNIQUE,

Descriptive Note:

Corporate Author:

UPPSALA UNIV (SWEDEN) QUANTUM CHEMISTRY GROUP

Personal Author(s):

Report Date:

1965-10-01

Pagination or Media Count:

45.0

Abstract:

The partitioning technique for solving the eigenvalue problem, H psi E psi, is briefly reviewed in matrix and operator form. It is shown that, if R is a real variable, one may construct a single- or multivalued function S fR such that each pair R and S bracket at least one true eigenvalue E. If R is chosen as an upper bound by means of the variation principle, the function S is hence going to provide a lower bound. The partitioning technique is here used to derive Brillouin-type and Schrodinger-type perturbation expansions and, in the case of a positive definite perturbation V0, upper and lower bounds for the sums are determined by means of operator inequalities. By using the method of inner projection, it is further shown that the remainders in the Brillouin-type expansion may be evaluated with any accuracy desired, and the corresponding problem for the Schrodinger-type expansion is briefly discussed. Numerical applications are given elsewhere. Author

Descriptors:

Subject Categories:

  • Numerical Mathematics
  • Quantum Theory and Relativity

Distribution Statement:

APPROVED FOR PUBLIC RELEASE