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Error bounds for expectation values: Some applications and extensions

Jennings, P. and Wilson Jr, E.B. (1967) Error bounds for expectation values: Some applications and extensions. The Journal of Chemical Physics, 47 (6). pp. 2130-2136.

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The error‐bound procedure of Bazley and Fox is extended as in a previous paper and applied to the expectation values of some quantum‐mechanical operators of physical interest. The quality of the bounds is discussed and it is found to be possible to improve them under certain conditions. An attempt is made to use these error‐bound formulas as variational principles for expectation values. Some special cases such as Fermi contact terms and electron densities are discussed separately. Errors in Hartree—Fock expectation values are considered from the point of view of Brillouin's theorem and some qualitative predictions of their magnitudes are made. Transition probabilities are also treated and some qualitative conclusions are made concerning the accuracy of the alternative length and velocity formulas.

Item Type: Journal Article
Publisher: American Institute of Physics
Copyright: © 1967 American Institute of Physics
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