Quantum Ergodicity and Delocalization of Schrödinger Eigenfunctions

This book deals with various topics in quantum chaos, starting with a historical introduction and then focussing on the delocalisation of eigenfunctions of Schrödinger operators for chaotic Hamiltonian systems. It contains a short introduction to microlocal analysis, necessary for proving the Shnirelman theorem and giving an account of the author's work on entropy of eigenfunctions on negatively curved manifolds. In addition, further work by the author on quantum ergodicity of eigenfunctions on large graphs is presented, along with a survey of results on eigenfunctions on the round sphere, as well as a rather detailed exposition of the result by Backhausz and Szegedy on the Gaussian distribution of eigenfunctions on random regular graphs. Like the lecture series it is based on, the text is aimed at all mathematicians, from the graduate level onwards, who want to learn some of the important ideas in the field.