  We propose a numerical method for evaluating eigenvalues and eigenfunctions
of Schr\"odinger operators with general confining potentials. The method is
selective in the sense that only the eigenvalue closest to a chosen input
energy is found through an absolutely-stable relaxation algorithm which has
rate of convergence infinite. In the case of bistable potentials the method
allows one to evaluate the fundamental energy splitting for a wide range of
tunneling rates.
