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arXiv · hep-th/9510096

Exact Solution of a N-body Problem in One Dimension

Avinash Khare
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Abstract

Complete energy spectrum is obtained for the quantum mechanical problem of N one dimensional equal mass particles interacting via potential $$V(x_1,x_2,...,x_N) = g\sum^N_{i < j}{1\over (x_i-x_j)^2} - {α\over \sqrt{\sum_{i < j} (x_i-x_j)^2}}$$ 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 $p'_i$ with $p'_i=p_{N+1-i}$.

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Avinash Khare. 1995-10-15. Exact Solution of a N-body Problem in One Dimension. https://doi.org/10.1088/0305-4470%2F29%2F19%2F029

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