dorsal/arxiv
View SchemaAn extended class of L2-series solutions of the wave equation
| Authors | A. D. Alhaidari |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0409002 |
| URL | https://arxiv.org/abs/quant-ph/0409002 |
| DOI | 10.1016/j.aop.2004.11.014 |
| Journal | Ann. Phys. 317.1 (2005) 152-174 |
Abstract
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such includes the discrete (for bound states) as well as the continuous (for scattering states) spectrum of the Hamiltonian. The problem translates into finding solutions of the resulting three-term recursion relation for the expansion coefficients of the wavefunction. These are written in terms of orthogonal polynomials, some of which are modified versions of known polynomials. The examples given, which are not exhaustive, include problems in one and three dimensions.
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"abstract": "We lift the constraint of a diagonal representation of the Hamiltonian by\nsearching for square integrable bases that support an infinite tridiagonal\nmatrix representation of the wave operator. The class of solutions obtained as\nsuch includes the discrete (for bound states) as well as the continuous (for\nscattering states) spectrum of the Hamiltonian. The problem translates into\nfinding solutions of the resulting three-term recursion relation for the\nexpansion coefficients of the wavefunction. These are written in terms of\northogonal polynomials, some of which are modified versions of known\npolynomials. The examples given, which are not exhaustive, include problems in\none and three dimensions.",
"arxiv_id": "quant-ph/0409002",
"authors": [
"A. D. Alhaidari"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.aop.2004.11.014",
"journal_ref": "Ann. Phys. 317.1 (2005) 152-174",
"title": "An extended class of L2-series solutions of the wave equation",
"url": "https://arxiv.org/abs/quant-ph/0409002"
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