Docentship lecture: Nonperturbative Quantum Mechanics and Geometry

Chairperson: Professor Ulf Danielsson

Representative of the Docentship Committee: Professor Carlos Pérez de los Heros

Abstract:

The evolution of a physical system is modeled, in the context of Mathematical Physics, by its equations of motion. Many of the equations governing fundamental laws of Nature are notoriously elegant, due to symmetries underlying conservation laws. However, behind the apparent simplicity of the equations often lies a rich landscape of dynamical behavior, whose scope can only be appreciated through the computation of exact solutions. Each solution describes a possible evolution of the system, and while some are easy to find and intuitive to understand, others can be ’hidden’ and can describe surprising phenomena. In this lecture we will discuss the framework of exact WKB analysis, a technique that allows to probe solutions to Schrödinger’s equation that lie beyond the reach of ordinary perturbation theory. I will also discuss a connection to the geometry of Riemann surfaces that emerges naturally within this framework, explaining how this leads to a comprehensive understanding of the space of solutions in all regions of parameter space.

The lecture is an obligatory teaching test for those applying for admittance as docent and it should be possible for students and others with basic academic education in the relevant field to follow it. The lecture lasts 40-45 minutes with subsequent discussion. The lecture will be given in English.