  Using a newly suggested algorithm of Gozzi, Reuter, and Thacker for
calculating the excited states of one dimensional systems, we determine
approximately the eigenvalues and eigenfunctions of the anharmonic oscillator,
described by the Hamiltonian $H= p^2/2 + g x^4$. We use ground state
post-gaussian trial wave functions of the form $\Psi(x) =
  N{\rm{exp}}[-b |x|^{2n}]$, where $n$ and $b$ are continuous variational
parameters. This algorithm is based on the hierarchy of Hamiltonians related by
supersymmetry (SUSY) and the factorization method. We find that our two
parameter family of trial wave functions yields excellent energy eigenvalues
and wave functions for the first few levels of the anharmonic oscillator.
