dorsal/arxiv
View SchemaLow-lying spectra in anharmonic three-body oscillators with a strong short-range repulsion
| Authors | Miloslav Znojil |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307239 |
| URL | https://arxiv.org/abs/quant-ph/0307239 |
| DOI | 10.1088/0305-4470/36/38/310 |
| Journal | J. Phys. A: Math. Gen. 36 (2003) 9929-9941 |
Abstract
Three-body Schroedinger equation is studied in one dimension. Its two-body interactions are assumed composed of the long-range attraction (dominated by the L-th-power potential) in superposition with a short-range repulsion (dominated by the (-K)-th-power core) plus further subdominant power-law components if necessary. This unsolvable and non-separable generalization of Calogero model (which is a separable and solvable exception at L = K = 2) is presented in polar Jacobi coordinates. We derive a set of trigonometric identities for the potentials which generalizes the well known K=2 identity of Calogero to all integers. This enables us to write down the related partial differential Schroedinger equation in an amazingly compact form. As a consequence, we are able to show that all these models become separable and solvable in the limit of strong repulsion.
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"abstract": "Three-body Schroedinger equation is studied in one dimension. Its two-body\ninteractions are assumed composed of the long-range attraction (dominated by\nthe L-th-power potential) in superposition with a short-range repulsion\n(dominated by the (-K)-th-power core) plus further subdominant power-law\ncomponents if necessary. This unsolvable and non-separable generalization of\nCalogero model (which is a separable and solvable exception at L = K = 2) is\npresented in polar Jacobi coordinates. We derive a set of trigonometric\nidentities for the potentials which generalizes the well known K=2 identity of\nCalogero to all integers. This enables us to write down the related partial\ndifferential Schroedinger equation in an amazingly compact form. As a\nconsequence, we are able to show that all these models become separable and\nsolvable in the limit of strong repulsion.",
"arxiv_id": "quant-ph/0307239",
"authors": [
"Miloslav Znojil"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/36/38/310",
"journal_ref": "J. Phys. A: Math. Gen. 36 (2003) 9929-9941",
"title": "Low-lying spectra in anharmonic three-body oscillators with a strong short-range repulsion",
"url": "https://arxiv.org/abs/quant-ph/0307239"
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