Gaussian effective potential: Computation of eigenvalues

The Gaussian effective potential (GEP) is an approximation to quantum mechanics that semiquantitatively estimates quantum effects such as zero-point fluctuations and tunneling. We show how to use the GEP to compute semiclassical eigenvalues. It is well known that the GEP provides very accurate variational approximations to the ground-state energy of simple quantum systems; our results show that it also provides accurate excited-state energies. We also show how this method is related to the first-order Bargmann-Voros coherent-state representation of quantum mechanics, and that our results improve upon those derived from the latter method.