EIGENSTATES OF THE GRAVITATIONAL SCHRÖDINGER EQUATION

Abstract

We develop a new algorithm to compute the eigenvalues and eigenfunctions of the gravitational Schrödinger equation. The nonlinear two-point boundary problem is solved by an inner–outer iteration and the resulting method is fast, readily parallelizable, and, unlike shooting methods, is able to compute eigenfunctions with a very large number (>50) of nodes. The theory and implementation of the method are discussed and it is applied to compute the s-wave spectrum of a gravitational Bose–Einstein condensate.