Hypervirial Functions and the Positive Powers of the Radial Coordinate Operator in He and H—

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Abstract
Ground‐state He and H— trial functions are scaled to satisfy the hypervirial relations generated by the family of hypervirial operators Wn=r1np1. These one‐parameter hypervirial functions are used to calculate expectation values of the positive powers of the radial coordinate operators, rt, for t=1 through 20. Accurate values of 〈rt〉, for this range of t, are calculated using 20‐term Hylleraas functions. A comparison of results shows that simple hypervirial functions of the form exp[—K(r1+r2)] scaled to satisfy the hypervirial relations generated by W2, give a good over‐all calculation of 〈rt〉 for both He and H—. The hypervirial theorem is used to develop a variety of expectation value relationships for one‐ and two‐electron central force problems in the Appendix.