Tight lower bounds to eigenvalues of the Schrödinger equation

A new tight lower bound to eigenvalues of the Schrödinger equation, which tends to be better than the well-known Temple lower bound, is presented. The new bound works (as does the Temple bound) for both ground and excited states. Optimization of both the Temple bound and the new tight bound with respect to a variational trial function is discussed. Numerical results are given for the anharmonic oscillator.