On the perturbation theory for spectra in quantum mechanics

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 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.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar