A recursive construction of joint eigenfunctions for the hyperbolic nonrelativistic Calogero-Moser Hamiltonians

Martin Hallnäs; Simon Ruijsenaars

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arXiv · 1305.4759

A recursive construction of joint eigenfunctions for the hyperbolic nonrelativistic Calogero-Moser Hamiltonians

Martin Hallnäs·Simon Ruijsenaars

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Abstract

We obtain symmetric joint eigenfunctions for the commuting PDOs associated to the hyperbolic Calogero-Moser N-particle system. The eigenfunctions are constructed via a recursion scheme, which leads to representations by multidimensional integrals whose integrands are elementary functions. We also tie in these eigenfunctions with the Heckman-Opdam hypergeometric function for the root system A_{N-1}.

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Martin Hallnäs, Simon Ruijsenaars. 2013-05-21. A recursive construction of joint eigenfunctions for the hyperbolic nonrelativistic Calogero-Moser Hamiltonians. https://arxiv.org/abs/1305.4759

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