Asymptotic series for anharmonic oscillator.
Alexander Foksha

Abstract: We consider the standard one-dimensional quantum anharmonic oscillator. Formal Raleigh-Schrodinger procedure gives us a serie for eigenvalues over non-negative powers of coupling constant. It is well known that the series is divergent and asymptotic. But in fact it contains all the information about perturbed eigenvalues, which can be recovered by the process of Borel summation. The summation of divergent series is quite important part of modern physics where in some cases asymptotic series is the only thing physicists have. I will speak about classical results on asymptotic series for eigenvalues of anharmonic oscillator and their possible generalizations to eigenfunctions and their zeros.