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Lower-bound energies and the Virial theorem in wave mechanics

Published online by Cambridge University Press:  24 October 2008

G. L. Caldow  and
C. A. Coulson
G. L. Caldow
Affiliation:
Mathematical Institute, Oxford
C. A. Coulson
Affiliation:
Mathematical Institute, Oxford
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Abstract

Several forms of the lower-bound variational method for the calculation of the eigenvalues in a wave-mechanical problem are considered, and compared; the particular case of the harmonic oscillator being chosen. All forms have certain unsatisfactory features, but some of them are considerably worse than others. One reason why calculations of lower bounds are in general less satisfactory than Ritz-type calculations of an upper bound is shown to be that whereas, in the presence of a scale factor, this latter wave-function satisfies the virial theorem, in none of the lower-bound wave-functions is this true. Similar calculations are reported for the ground state of the helium atom.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 2 , April 1961 , pp. 341 - 347
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

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