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arXiv · 2305.00791

Wave functions for quantum integrable particle systems via partial confluences of multivariate hypergeometric functions

Jan Felipe van Diejen·Erdal Emsiz
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Abstract

Starting from the hyperoctahedral multivariate hypergeometric function of Heckman and Opdam (associated with the $BC_n$ root system), we arrive -- via partial confluent limits in the sense of Oshima and Shimeno -- at solutions of the eigenvalue equations for the Toda chain with one-sided boundary perturbations of P\"oschl-Teller type and for the hyperbolic Calogero-Sutherland system in a Morse potential. With the aid of corresponding degenerations of the (bispectral dual) difference equations for the Heckman-Opdam hyperoctahedral hypergeometric function, it is deduced that the eigensolutions in question are holomorphic in the spectral variable.

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Jan Felipe van Diejen, Erdal Emsiz. 2023-05-01. Wave functions for quantum integrable particle systems via partial confluences of multivariate hypergeometric functions. https://doi.org/10.1016/j.jde.2019.10.033

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