SUSY-based variational method for the anharmonic oscillator

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= {1}/{2}p ²+gx ⁴. We use ground state post-Gaussian trial wave functions of the form Ψ( x)= N exp(- b| x| ^{2 n}), 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.