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

Abstract

It is proved that if the Schrödinger equation $L\psi =\lambda \psi$ of Calogero-Moser-Sutherland type with $$L=-\Delta +\sum _{\alpha \in {\mathcal{A}}_{+}}\frac{m_{\alpha }(m_{\alpha }+1)(\alpha ,\alpha )}{{\sin }^2(\alpha ,x)}$$ has a solution of the product form ${\psi }_0={\prod }_{\alpha \in {\mathcal{A}}_{+}}{\sin }^{-m_{\alpha }}(\alpha ,x),$ then the function $F(x)=\sum _{\alpha \in {\mathcal{A}}_{+}}{m}_{\alpha }(\alpha ,x{)}^2\log (\alpha ,x{)}^2$ satisfies the generalised WDVV equations.

10 pages

References in corpus (3)

• Locus configurations and $\vee$-systems
• Superanalogs of the Calogero operators and Jack polynomials
• On geometry of a special class of solutions to generalised WDVV equations

Cited by in corpus (4)

• Deformed quantum Calogero-Moser problems and Lie superalgebras
• Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems
• On the geometry of V-systems
• V-systems, holonomy Lie algebras and logarithmic vector fields