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Ehrenfest's theorem and the (generalized) TRK sum rule for variational wavefunctions
1.D. J. Thouless, Nucl. Phys. 22, 78 (1961);
1.A. D. McLachlan and M. A. Ball, Rev. Mod. Phys. 36, 844 (1964);
1.R. A. Harris, J. Chem. Phys. 50, 3947 (1969).
2.A. Dalgarno and S. T. Epstein, J. Chem. Phys. 50, 2837 (1969).
3.The zero order terms yield the hypervirial relation Similarly the zero order terms in (1) yield the hypervirial relation
4.See S. T. Epstein and R. E. Johnson, J. Chem. Phys. 51, 188 (1969).
5.Reference 4, Footnote 7.
6.Of course if ν is a one‐electron function of coordinates only, then, for the usual will automatically be a one‐electron operator.
7.Thus in the class of theories discussed by S. T. Epstein, J. Phys. B 5, 741 (1972), a class which includes time‐dependent unrestricted Hartree‐Fock and CI, if the right hand side of (8) is among the possible in the set of trial functions, then it is easy to show that (8) will be satisfied.
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