mini-cours : Solving Schrodinger equation with polynomial potential

Mardi 23 mai 2017 14:00-15:30 - Dmytro Volin

mini-cours : Solving Schrodinger equation with polynomial potential

Résumé : Our final goal is to demonstrate that the spectrum of Schrodinger operator with polynomial potential is given by the roots of certain Bethe equations.
In the part 1 of the course (monday, May 22) we will discuss analytic properties of the solutions of Schrodinger equation (wave functions) as holomorphic functions in the complex plane. A particular attention will be given to behaviour of the wave functions at infinity where they can be approximated by quasiclassical=eikonal=WKB expressions and where Stokes phenomena emerges. We will finish by deriving Bohr-Sommerfeld quantisation conditions using arguments of analytic continuation in the complex plane.
In the part 2 of the course (Tuesday, May 23) we will introduce the notion of spectral determinants, study their analytic properties and derive Bethe equations that fix zeros of these determinants. Derivation itself will exploit the analytic properties of wave functions introduced in part 1. We will finish with numerical solution of the Bethe equations and, if time permits, discuss generalisations of this formalism known as ODE/IM correspondence.

Lieu : Salle René Baire

Pour en savoir plus sur cet événement, consultez l'article Séminaires Math-Physique