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Sum Rules for Variational Wavefunctions
1.J. O. Hirschfelder, S. T. Epstein, and W. B. Brown, Advan. Quantum Chem. 1, 256 (1964).
2.H. J. Kolker and H. H. Michels, J. Chem. Phys. 43, 1027 (1965).
3.M. Karplus and H. J. Kolker, J. Chem. Phys. 38, 1263 (1963).
4.Y. M. Chan and A. Dalgarno, Proc. Phys. Soc. (London) 86, 777 (1965).
5.The proof as given assumes that is known exactly. Chan and Dalgarno adopted an approximate form of but in effect replaced the exact Hamiltonian by an approximate Hamiltonian of which was an exact eigenfunction. Since their approximate Hamiltonian contained only local potentials, the sum rule (25) was still satisfied exactly.
6.More generally if and are in the set, , .
7.A. Dalgarno, Advan. Phys. 11, 281 (1962).
8.P. W. Langhoff, M. Karplus, and R. P. Hurst, J. Chem. Phys. 44, 505 (1966).
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