Exact Heisenberg operator solutions for multiparticle quantum mechanics

Abstract

Exact Heisenberg operator solutions for independent “sinusoidal coordinates” as many as the degree of freedom are derived for typical exactly solvable multiparticle quantum mechanical systems, the Calogero systems [J. Math. Phys. 12, 419 (1971)] based on any root system. These Heisenberg operator solutions also present the explicit forms of the annihilation-creation operators for various quanta in the interacting multiparticle systems. At the same time they can be interpreted as multivariable generalization of the three term recurrence relations for multivariable orthogonal polynomials constituting the eigenfunctions.