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 = 1/2p2+gx4. We use ground state post-Gaussian trial wave functions of the form PSI(x) = N 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.