Upper Bounds to the Overlap of Approximate and Exact Wavefunctions

One measure of how accurately an approximate wavefunction approximatesthe true wavefunction is the overlap of the two functions. In general the truewavefunction is not known so this overlap cannot be directly calculated. Wederive two methods from the t expansion of Horn and Weinstein to bound fromabove the magnitude of the overlap of an approximate wavefunction with theground state. The first method relies on the ability to divide the Hamiltonian intoa base problem and a perturbation. The second method is more general and seemsmuch more promising.