Bounds on Weighted Mean Errors of Approximate Wave Functions. I. Theory
Isao Shimamura · Journal of the Physical Society of Japan · 1970
Weighted mean errors are defined and proposed as criteria of the error in an approximate wave function for an arbitrary state. Upper and lower bounds on the weighted mean errors are derived, and properties of and relations among the bounds are discussed. The Eckart and the James-Coolidge criteria are shown to be special cases of some of the bounds.