Abstract
The purpose of this note is to recall the theory of the (homogenized) spectral problem for Schrodinger equation with a polynomial potential and its relation with quadratic differentials. We derive from results of this theory that the accumulation rays of the eigenvalues of the latter problem are in \(1-1\)-correspondence with the short geodesics of the singular planar metrics induced by the corresponding quadratic differential. We prove that for a polynomial potential of degree \(d,\) the number of such accumulation rays can be any positive integer between \((d-1)\) and \(d \atopwithdelims ()2\).
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