On Series Expansion of a Determinant and Solution of the Secular Equation
- 1 January 1966
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 7 (1) , 27-34
- https://doi.org/10.1063/1.1704810
Abstract
A determinant and its cofactors are expanded in terms of the cyclic products of its elements. With the aid of this expansion, an implicit equation for the eigenvalue and an explicit equation for amplitudes of the corresponding eigenfunction are obtained, respectively, in terms of a ratio of two simple series expansions. Comparisons with Feenberg's perturbation formula and with Sasakawa's perturbation method are also discussed.Keywords
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