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We present a new family of the locus configurations which is not related to -systems thus giving the answer to one of the questions raised by one of the authors about the relation between the generalised quantum Calogero-Moser systems and special solutions of the generalised WDVV equations. As a by-product we have new examples of the hyperbolic equations satisfying the Huygens' principle in the...
We consider a class of multidimensional Schrödinger operators L=−Δ+u(x) which can be intertwined with the quantum harmonic oscillator L 0 =−Δ+ω 2 x 2 : LD=D(L 0 +λ) for some partial differential operator D and constant λ. The corresponding potentials are rational with the second order poles along some hyperplanes. A sufficient condition for the existence of D is given...