On generalisations of Calogero-Moser-Sutherland quantum problem and WDVV equations

Details On generalisations of Calogero-Moser-Sutherland quantum problem and WDVV equations On generalisations of Calogero-Moser-Sutherland quantum problem and WDVV equations

2002-04-26

arxiv.org/abs/math-ph/0204050v1

Physics

Mathematical Physics

10 pages

Scientific paper

It is proved that if the Schr\"odinger equation $L \psi = \lambda \psi$ of Calogero-Moser-Sutherland type with $$L = -\Delta + \sum\limits_{\alpha\in{\cal A}_{+}} \frac{m_{\alpha}(m_{\alpha}+1) (\alpha,\alpha)}{\sin^{2}(\alpha,x)}$$ has a solution of the product form $\psi_0 = \prod_{\alpha \in {\cal {A}_+}} \sin^{-m_{\alpha}}(\alpha,x),$ then the function $F(x) =\sum\limits_{\alpha \in \cal {A}_{+}} m_{\alpha} (\alpha,x)^2 {\rm log} (\alpha,x)^2$ satisfies the generalised WDVV equations.

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