Accession Number : AD0464263


Title :   LOWER BOUNDS FOR EIGENVALUES


Descriptive Note : Technical rept.


Corporate Author : HARVARD UNIV CAMBRIDGE MA MALLINCKRODT LAB


Personal Author(s) : Wilson, Jr, E B


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/464263.pdf


Report Date : Jan 1965


Pagination or Media Count : 15


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.


Descriptors :   *FUNCTIONS(MATHEMATICS) , *MOLECULAR STRUCTURE , *EIGENVALUES , HELIUM , SERIES(MATHEMATICS) , STATISTICAL MECHANICS , MAPPING(TRANSFORMATIONS) , HAMILTONIAN FUNCTIONS , ATOMIC STRUCTURE , MOLECULAR ELECTRONICS , INTEGRALS , QUANTUM THEORY , EXCITATION , GROUND STATE


Subject Categories : Atomic and Molecular Physics and Spectroscopy


Distribution Statement : APPROVED FOR PUBLIC RELEASE