Exact diagonalization of 1D interacting spinless Fermions

We acquire a method of constructing an infinite set of exact eigenfunctions of 1D interacting spinless Fermionic systems. Creation and annihilation operators for the interacting system are found and thereby the many-body Hamiltonian is diagonalized. 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.