SUSY-Based Variational Method for the Anharmonic Oscillator

Details SUSY-Based Variational Method for the Anharmonic Oscillator SUSY-Based Variational Method for the Anharmonic Oscillator

1994-02-17

arxiv.org/abs/patt-sol/9402002v1

Nonlinear Sciences

Pattern Formation and Solitons

9 pages, LaTeX, 2 Figures (request), to be published in Physics Letters A

Scientific paper

10.1016/0375-9601(94)90051-5

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.

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