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Integrability in the theory of Schrödinger operator and harmonic analysis

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Abstract

The algebraic integrability for the Schrödinger equation in ℝn and the role of the quantum Calogero-Sutherland problem and root systems in this context are discussed. For the special values of the parameters in the potential the explicit formula for the eigenfunction of the corresponding Sutherland operator is found. As an application the explicit formula for the zonal spherical functions on the symmetric spacesSU *2n /Spn (type A II in Cartan notations) is presented.

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Authors and Affiliations

  1. Department of Mathematics and Mechanics, Moscow State University, 119899, Moscow, Russia

    Oleg A. Chalykh & Alexander P. Veselov

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  1. Oleg A. Chalykh
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  2. Alexander P. Veselov
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Communicated by N.Yu. Reshetikhin

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Chalykh, O.A., Veselov, A.P. Integrability in the theory of Schrödinger operator and harmonic analysis. Commun.Math. Phys. 152, 29–40 (1993). https://doi.org/10.1007/BF02097056

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  • DOI: https://doi.org/10.1007/BF02097056

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