Variational approach to the Schrödinger equation with a delta-function potential

Abstract

We obtain accurate eigenvalues of the one-dimensional Schrödinger equation with a Hamiltonian of the form $H_g=H+g\delta (x)$, where $\delta (x)$ is the Dirac delta function. We show that the well known Rayleigh-Ritz variational method is a suitable approach provided that the basis set takes into account the effect of the Dirac delta on the wavefunction.