Exact Solution of a N-body Problem in One Dimension

Abstract

Complete energy spectrum is obtained for the quantum mechanical problem of N one dimensional equal mass particles interacting via potential $$V(x_1,x_2,...,x_N)=g\sum _{i<j}^N\frac{1}{(x_i-x_j{)}^2}-\frac{\alpha }{\sqrt{{\sum }_{i<j}(x_i-x_j{)}^2}}$$ Further, it is shown that scattering configuration, characterized by initial momenta $p_i(i=1,2,...,N)$ goes over into a final configuration characterized uniquely by the final momenta $p_i^{\prime }$ with $p_i^{\prime }=p_{N+1-i}$.

8 pages, tex file, no figures, sign in the first term on the right hand side of eq.3 corrected

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