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Recursion Relations for Coulomb Matrix Elements
1.See H. B. Bebb, J. Math. Phys. 7, 955 (1966), and references therein.
2.For an application of this method to the calculation of diagonal matrix elements, see J. H. Epstein and S. T. Epstein, Am. J. Phys. 30, 266 (1962).
3.For some cautionary remarks concerning the use of such identities, see S. L. Gordon, J. Chem. Phys. 42, 4184 (1965), Appendix IC.
5.Specializing to the case one can, by use of (5) and (6), give a very simple derivation of the Pasternack‐Sternheimer theorem [J. Math. Phys. 3, 1280 (1962)].
6.See, for example, E. Merzbacher, Quantum Mechanics (John Wiley & Sons, Inc., New York, 1961), p. 161.
7.Results for (see Ref. 1), and for hydrogen, and for the isotropic harmonic oscillator, are given in the technical report WIS‐TCI‐191, available on request from the Reprint Librarian of the Theoretical Chemistry Institute, University of Wisconsin, Madison, Wisconsin.
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