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An alternative formalism for the method of intermediate Hamiltonians

โœ Scribed by R. A. Sack

Publisher
John Wiley and Sons
Year
1972
Tongue
English
Weight
509 KB
Volume
6
Category
Article
ISSN
0020-7608

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โœฆ Synopsis

Abstract

The methods of intermediate Hamiltonians and of inner projections for the determination of lower bounds of eigenvalues of a Hermitian operator H are analysed and reformulated as linear matrix problems. Submatrices T which are only defined implicitly through the product TT^dฬŠ^ are best represented in triangular form. If the subspace complementary to the subspace determining the inner projection can be subdivided with different lower bounds for H, the bounds for the eigenvalues can be further improved. The new formalism is applied to obtain crude lower bounds for the ground state of the helium atom, using only 2 ร— 2 and 3 ร— 3 matrices.

๐Ÿ“œ SIMILAR VOLUMES

On an application of the intermediate Ha
On an application of the intermediate Hamiltonian method for molecular systems
โœ Rikuzo Seto; Ivan V. Stankevich ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 188 KB ๐Ÿ‘ 2 views

An application of the intermediate Hamiltonian method is reported in estimation of the lower bounds to the potential energy curve of the hydrogen molecule ion. An improvement of the method and its limitation are also discussed.

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An Alternative Numerical Method for Initial Value Problems Involving the Contact Nonlinear Hamiltonians
โœ Marijan Koลกtrun; Juha Javanainen ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 71 KB

We suggest a new difference scheme for dealing with contact nonlinear Hamiltonians. The scheme has two parts. First, the system is transformed to the interaction picture of quantum mechanics using the time-independent Hamiltonian H 0 . This reduces the problem to a system of ordinary differential eq