Lower bounds for eigenvalues. Technical report
Technical Report
·
OSTI ID:6473424
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.
- Research Organization:
- Harvard Univ., Cambridge, MA (USA). Mallinckrodt Lab.
- OSTI ID:
- 6473424
- Report Number(s):
- AD-464263
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
640302* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
74 ATOMIC AND MOLECULAR PHYSICS
CALCULATION METHODS
CRYOGENIC FLUIDS
EIGENVALUES
ELEMENTS
ENERGY LEVELS
FLUIDS
GROUND STATES
HELIUM
LIMITING VALUES
MATHEMATICAL OPERATORS
MOLECULAR STRUCTURE
NONMETALS
PROJECTION OPERATORS
RARE GASES
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
74 ATOMIC AND MOLECULAR PHYSICS
CALCULATION METHODS
CRYOGENIC FLUIDS
EIGENVALUES
ELEMENTS
ENERGY LEVELS
FLUIDS
GROUND STATES
HELIUM
LIMITING VALUES
MATHEMATICAL OPERATORS
MOLECULAR STRUCTURE
NONMETALS
PROJECTION OPERATORS
RARE GASES