Low-lying spectra in anharmonic three-body oscillators with a strong short-range repulsion
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Publication:4468595
DOI10.1088/0305-4470/36/38/310zbMATH Open1057.81020arXivquant-ph/0307239OpenAlexW1991975790MaRDI QIDQ4468595
Publication date: 10 June 2004
Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/quant-ph/0307239
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Many-body theory; quantum Hall effect (81V70)
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