Selberg correlation integrals and the [formula omitted] quantum many-body system

Abstract

A class of multidimensional integrals known as Selberg correlation integrals are shown to be of relevance to the one-dimensional quantum many-body system with the 1 r 2 pair potential. It is shown that limiting forms of the correlation integrals give exact wave functions of the quantum hamiltonian, and that the density matrix and the two-particle density-density distribution of the ground state wave function can be expressed in terms of these integrals. Known exact expressions for the correlation integrals allow exact evaluations of the latter quantities to be given in terms of generalized hypergeometric functions.