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Convergence in lower bound formulae

Published online by Cambridge University Press:  24 October 2008

Mary Walmsley
Mary Walmsley
Affiliation:
Mathematical Institute, Oxford
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Abstract

A convergence criterion is applied to the eigenvalue problems, which occur in lower bound calculations for , when either the energy or the nuclear charge is taken as the eigenvalue. In the former problem the lower bounds do not converge to the exact energy and the continuum causes a larger error for σu (1) than for σg (1). However, when the nuclear charge is taken as the eigenvalue the lower bound procedure converges.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 2 , April 1967 , pp. 451 - 455
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Bazley, N. W.Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 850–853.CrossRefGoogle Scholar
(2)Bazley, N. W.Phys. Rev. 120 (1960), 144–149.CrossRefGoogle Scholar
(3)Bazley, N. W.J. Math. Mech. 10 (1961), 289–307.Google Scholar
(4)Bazley, N. W. and Fox, D. W.J. Res. Nat. Bur. Standards 65B (1961), 105–111.CrossRefGoogle Scholar
(5)Bazley, N. W. and Fox, D. W.Phys. Rev. 124 (1961), 483–492.CrossRefGoogle Scholar
(6)Bazley, N. W. and Fox, D. W.J. Math. Phys. 3 (1962), 469–471.CrossRefGoogle Scholar
(7)Bazley, N. W. and Fox, D. W.Arch. Rational Mech. Anal. 10 (1962), 352–360.CrossRefGoogle Scholar
(8)Bazley, N. W. and Fox, D. W.Rev. Mod. Phys. 35 (1963), 712–716.CrossRefGoogle Scholar
(9)Bazley, N. W. and Fox, D. W.J. Math. Phys. 4 (1963), 1147–1153.CrossRefGoogle Scholar
(10)Coulson, C. A. and Johnson, B. P.Proc. Phys. Soc. 84 (1964), 263–268.CrossRefGoogle Scholar
(11)Coulson, C. A. and Walmsley, M.Proc. Cambridge Philos. Soc. 62 (1966), 769–776.Google Scholar
(12)Riesz, F. and Sz-Nagy, B.Functional Analysis. Page 372 (1956 edition).Google Scholar
(13)Bates, D. R., Ledsham, K. and Stewart, A. L.Philos. Trans. Roy. Soc. London Ser. A 246 (1953), 215–240.Google Scholar