Integral equations: A tool to solve the Schrödinger equation (Q1086992)

From the integral equation equivalent to the one-dimensional Schrödinger equation with the boundary conditions appropriate for a bound state problem, an exact three-point integration rule is derived. The approximate of this rule by means of the Euler-McLaurin sum rule gives rise to various \(O(h^ 2)\) and \(O(h^ 4)\) integration methods associated with the different ways of splitting the starting equation into a free part and an interaction term. The method is particularly useful to deal with the singularities of the potential.