Weinstein Calculations for Excited States

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Abstract
Weinstein's principle for an energy level, 〈H〉—Q≤Ej≤〈H〉+Q, gives both a lower and an upper bound and is applicable to both ground and excited states. Here, Q2=〈(H—〈H〉)2〉, all expectation values being calculated with respect to the same approximate wavefunction. An iterative method is proposed for solution of the necessary nonlinear equations. In tests on H2+ and H2, it is shown that the iterative method is workable, and that fair lower bounds are obtained. A formal perturbation theory is used to partly explain our results. Comparisons are made with the conventional variation method.