Addendum to ‘Selberg correlation integrals and the 1/ r2 quantum many body system’

Abstract

Two new results relating Jack symmetric polynomials, and n-dimensional hypergeometric functions based on Jack symmetric polynomials, to the 1/ r 2 quantum many body system in periodic boundary conditions are obtained. The first result is that all excited states in the quantum system can be written as the product of the ground-state wave function and a Jack symmetric polynomial. The second result expresses the ground-state two-particle distribution and one-body density matrix in the N-particle system, for even values of the coupling γ, as γ- and 1 2 γ- dimensional integrals respectively.