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PIRSA:21110011

Video URL

https://pirsa.org/21110011

On the perturbation theory for spectra in quantum mechanics

          @misc{ scivideos_PIRSA:21110011,
            doi = {10.48660/21110011},
            url = {https://pirsa.org/21110011},
            author = {Kontsevich, Maxim},
            keywords = {Mathematical physics},
            language = {en},
            title = {On the perturbation theory for spectra in quantum mechanics},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2021},
            month = {nov},
            note = {PIRSA:21110011 see, \url{https://scivideos.org/pirsa/21110011}}
          }

Maxim Kontsevich Institut des Hautes Etudes Scientifiques (IHES)

Talk numberPIRSA:21110011
DOI10.48660/21110011
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

Consider a polynomial differential operator in one variable, depending on a small parameter (Planck constant). Under appropriate conditions, the low-energy spectrum admits an asymptotic expansion in hbar.
I will present a way to calculate such a series via a purely "commutative problem", a mixture of variations of Hodge structures and of the Stirling formula. This result came from discussions with A.Soibelman. It seems that we obtain an explanation of an old observation by J.Zinn-Justin of the 

 universal appearance of Bernoulli numbers.