dorsal/arxiv
View SchemaSUSY-Based Variational Method for the Anharmonic Oscillator
| Authors | Fred Cooper, John Dawson, Harvey Shepard |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9402002 |
| URL | https://arxiv.org/abs/patt-sol/9402002 |
| DOI | 10.1016/0375-9601(94)90051-5 |
Abstract
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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"abstract": "Using a newly suggested algorithm of Gozzi, Reuter, and Thacker for\ncalculating the excited states of one dimensional systems, we determine\napproximately the eigenvalues and eigenfunctions of the anharmonic oscillator,\ndescribed by the Hamiltonian $H= p^2/2 + g x^4$. We use ground state\npost-gaussian trial wave functions of the form $\\Psi(x) =\n N{\\rm{exp}}[-b |x|^{2n}]$, where $n$ and $b$ are continuous variational\nparameters. This algorithm is based on the hierarchy of Hamiltonians related by\nsupersymmetry (SUSY) and the factorization method. We find that our two\nparameter family of trial wave functions yields excellent energy eigenvalues\nand wave functions for the first few levels of the anharmonic oscillator.",
"arxiv_id": "patt-sol/9402002",
"authors": [
"Fred Cooper",
"John Dawson",
"Harvey Shepard"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1016/0375-9601(94)90051-5",
"title": "SUSY-Based Variational Method for the Anharmonic Oscillator",
"url": "https://arxiv.org/abs/patt-sol/9402002"
},
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