A new expansion method in the Feynman path integral formalism: Application to a one-dimensional delta-function potential

Abstract

An expansion method in the path‐integral formulation of quantum mechanics, as proposed in a previous paper, is extended to account for states with odd parity. The method is tested on the case of a one‐dimensional attractive delta‐function potential and the well‐known solutions for both bound and scattering states are obtained analytically by an exact summation of the expansion series. The applicability of the method is discussed and it is shown how the energy spectrum could be determined by means of Stieltjes theory of moments.