Simon Ruijsenaars (Leeds University): A recursive construction of joint eigenfunctions for the N commuting hyperbolic Calogero-Moser Hamiltonians
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Europe/Budapest
Tanacsterem
Tanacsterem
Description
We present a recursive scheme that yields an explicit diagonalisation of the hyperbolic N-particle Calogero-Moser quantum systems of nonrelativistic and relativistic type. For the nonrelativistic case, the first step of the scheme yields the well-known 2-particle eigenfunction, which amounts to a specialization of the Gauss hypergeometric function. The work on the N>2 case (together with Martin Halln\"as) gives rise to an elementary representation of the joint eigenfunctions previously obtained (for root system A_{N-1}) by Heckman and Opdam. Last but not least, we briefly sketch a similar recursive construction for the joint eigenfunctions of the 2N commuting relativistic Calogero-Moser Hamiltonians.