Lower Bounds for Eigenvalues
- 15 November 1965
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 43 (10) , S172-S174
- https://doi.org/10.1063/1.1701482
Abstract
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.Keywords
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