Abstract
A theorem is presented which allows one to obtain a bound on the ground-state eigenvalue of an operator equation, given the eigenvalue of another related equation. The equations are related by the «potential» in one equation being the square of the «potential» in the other. The theorem is related to the Ritz variational principle, but allows one to obtain the bound without having to integrate a «trial function». Some examples are given of the application of this theorem to the Schrödinger equation.
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