Upper bounds to the overlap of approximate and exact wavefunctions

摘要

One measure of how accurately an approximate wavefunction approximates the true wavefunction is the overlap of the two functions. In general the true wavefunction is not known so this overlap cannot be directly calculated. We derive two methods from the t expansion of Horn and Weinstein to bound from above the magnitude of the overlap of an approximate wavefunction with the ground state. The first method relies on the ability to divide the Hamiltonian into a base problem and a perturbation. The second method is more general and seems much more promising. [References: 8]