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The Calogero-Moser equation system and the ensemble average in the Gaussian ensembles

H. -J. Stoeckmann
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Abstract

From random matrix theory it is known that for special values of the coupling constant the Calogero-Moser (CM) equation system is nothing but the radial part of a generalized harmonic oscillator Schroedinger equation. This allows an immediate construction of the solutions by means of a Rodriguez relation. The results are easily generalized to arbitrary values of the coupling constant. By this the CM equations become nearly trivial. As an application an expansion for in terms of eigenfunctions of the CM equation system is obtained, where X and Y are matrices taken from one of the Gaussian ensembles, and the brackets denote an average over the angular variables.

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H. -J. Stoeckmann. 2003-10-09. The Calogero-Moser equation system and the ensemble average in the Gaussian ensembles. https://doi.org/10.1088/0305-4470%2F37%2F1%2F009

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