Project 1: Toy models of quantum mechanics
The plan of this project is to study toy models of quantum mechanics associated to finite graphs. These models allow for an understanding of part of the mathematical structure of quantum mechanics, without the analytical complications that arise in the study of infinite dimensional Hilbert spaces. The project will focus on computations and examples, and on the path integral approach to the discrete version of Selberg’s trace formula . A good introduction to thes models is .