dorsal/arxiv
View SchemaVariational Interpolation Algorithm between Weak- and Strong-Coupling Expansions
| Authors | H. Kleinert |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9507005 |
| URL | https://arxiv.org/abs/quant-ph/9507005 |
| DOI | 10.1016/0375-9601(95)00683-T |
| Journal | Phys.Lett. A207 (1995) 133 |
Abstract
For many physical quantities, theory supplies weak- and strong-coupling expansions of the types $\sum a_n \alpha ^n$ and $ \alpha ^p\sum b_n (\alpha^{-2/q) ^n$, respectively. Either or both of these may have a zero radius of convergence. We present a simple interpolation algorithm which rapidly converges for an increasing number of known expansion coefficients. The accuracy is illustrated by calculating the ground state energies of the anharmonic oscillator using only the leading large-order coefficient $b_0$ (apart from the trivial expansion coefficent $a_0=1/2$). The errors are less than 0.5 for all g. The algorithm is applied to find energy and mass of the Fr\"ohlich-Feynman polaron. Our mass is quite different from Feynman's variational approach.
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"abstract": "For many physical quantities, theory supplies weak- and strong-coupling\nexpansions of the types $\\sum a_n \\alpha ^n$ and $ \\alpha ^p\\sum b_n\n(\\alpha^{-2/q) ^n$, respectively. Either or both of these may have a zero\nradius of convergence. We present a simple interpolation algorithm which\nrapidly converges for an increasing number of known expansion coefficients. The\naccuracy is illustrated by calculating the ground state energies of the\nanharmonic oscillator using only the leading large-order coefficient $b_0$\n(apart from the trivial expansion coefficent $a_0=1/2$). The errors are less\nthan 0.5 for all g. The algorithm is applied to find energy and mass of the\nFr\\\"ohlich-Feynman polaron. Our mass is quite different from Feynman\u0027s\nvariational approach.",
"arxiv_id": "quant-ph/9507005",
"authors": [
"H. Kleinert"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/0375-9601(95)00683-T",
"journal_ref": "Phys.Lett. A207 (1995) 133",
"title": "Variational Interpolation Algorithm between Weak- and Strong-Coupling Expansions",
"url": "https://arxiv.org/abs/quant-ph/9507005"
},
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