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An alternative formalism for the method of intermediate Hamiltonians
Author(s) -
Sack R. A.
Publication year - 1972
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560060516
Subject(s) - eigenvalues and eigenvectors , subspace topology , hermitian matrix , formalism (music) , mathematics , ground state , helium atom , combinatorics , coupled cluster , pure mathematics , quantum mechanics , physics , helium , mathematical analysis , molecule , visual arts , art , musical
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 d̊ 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 × 2 and 3 × 3 matrices.