Euclidean time formulation of the eigenvalue moment method: a moment problem-convexity analysis of Barnsley's theorem

Abstract

Over the last few years, the eigenvalue moment method (EMM) has been shown to be very effective in generating converging lower and upper bounds to the discrete low-lying spectrum of singular multidimensional Hamiltonians. In this work the authors adapt the EMM approach to the Euclidean time-dependent Schrodinger equation. The result is a new EMM theory which significantly overlaps with other eigenenergy bounding theories and which leads to a more rigorous algorithmic formulation than previously available.