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Brackets to the eigenvalues of the schrödinger equation, Part 2. Partial tridiagonalization of bandmatrices
Author(s) -
Weltin E.
Publication year - 2009
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.560050880
Subject(s) - tridiagonal matrix , eigenvalues and eigenvectors , mathematics , unitary state , matrix (chemical analysis) , unitary matrix , mathematical physics , schrödinger equation , mathematical analysis , pure mathematics , physics , quantum mechanics , chemistry , law , chromatography , political science
The range of application of the method of comparison‐matrices for the calculation of brackets to eigenvalues of the Schrödinger equation is extended to infinite bandmatrices, H. It is shown by construction that the elements α i and β i +1 of an infinite tridiagonal matrix may be calculated up to some finite maximum index, i , in a finite calculation. The tridiagonal matrix is a unitary transform of H and consequently has the same eigenvalues.