INTEGRABILITY IN THE THEORY OF SCHRODINGER OPERATOR AND HARMONIC-ANALYSIS

The algebraic integrability for the Schrodinger equation in R(n) 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 spaces SU2n*/Sp(n) (type All in Cartan notations) is presented.