  We acquire a method of constructing an infinite set of exact eigenfunctions
of 1--d interacting spinless Fermionic systems. Creation and annihilation
operators for the interacting system are found and thereby the many--body
Hamiltonian is diagonalised. The formalism is applied to several examples. One
example is the theory of Jack polynomials. For the Calogero-Moser-Sutherland
Hamiltonian a direct proof is given that the asymptotic Bethe Ansatz is
correct.
