dorsal/arxiv
View SchemaArbitrarily Accurate Eigenvalues for General Anharmonic Potentials
| Authors | Y. Meurice |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0202047 |
| URL | https://arxiv.org/abs/quant-ph/0202047 |
| DOI | 10.1088/0305-4470/35/41/314 |
| Journal | J.Phys.A35:8831-8846,2002 |
Abstract
We show that the Riccati form of the Schrodinger equation can be reformulated in terms of two linear equations depending on an arbitrary function G. When $G$ and the potential are polynomials, the solutions of these two equations are entire functions (L and K) and the zeroes of K are identical to those of the wave function. Requiring such a zero at a large but finite value of the argument yields the low energy eigenstates with exponentially small errors. Judicious choice of G can improve dramatically the numerical treatment. The method yields many significant digits with modest computer means.
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"abstract": "We show that the Riccati form of the Schrodinger equation can be reformulated\nin terms of two linear equations depending on an arbitrary function G. When $G$\nand the potential are polynomials, the solutions of these two equations are\nentire functions (L and K) and the zeroes of K are identical to those of the\nwave function. Requiring such a zero at a large but finite value of the\nargument yields the low energy eigenstates with exponentially small errors.\nJudicious choice of G can improve dramatically the numerical treatment. The\nmethod yields many significant digits with modest computer means.",
"arxiv_id": "quant-ph/0202047",
"authors": [
"Y. Meurice"
],
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"quant-ph",
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"physics.comp-ph"
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"doi": "10.1088/0305-4470/35/41/314",
"journal_ref": "J.Phys.A35:8831-8846,2002",
"title": "Arbitrarily Accurate Eigenvalues for General Anharmonic Potentials",
"url": "https://arxiv.org/abs/quant-ph/0202047"
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