Exact solution of an N-body problem in one dimension

Abstract

A complete energy spectrum is obtained for the quantum mechanical problem of N one-dimensional equal mass particles interacting via potential V(x₁, x₂,.....,x_N)=g∑^N_i<j 1/(x_i-x_j)²-α/√∑_i<j (x_i-x_j)². Furthermore, it is shown that the scattering configuration, characterized by initial momenta p(i=1,2,....N) , goes over into a final configuration characterized uniquely by the final momenta P'_i with P'_i=P_N+1-i.