Root Asymptotics of Spectral Polynomials

Abstract

We have been studying the asymptotic energy distribution of the algebraic part of the spectrum of the one-dimensional sextic anharmonic oscillator. We review some (both old and recent) results on the multiparameter spectral problem and show that our problem ranks among the degenerate cases of Heine-Stieltjes spectral problem, and we derive the density of the corresponding probability measure.