Semiclassical series expansion for wavefunctions in Schroedinger quantum field theories

In this talk, I will describe a semiclassical expansion for quantum wavefunctions in which the leading order semiclassical state is a decaying exponential, and higher-order quantum corrections are given by a recursive sequence of linear differential equations. This expansion technique has broad applicability not only to Schroedinger quantizations of finite-dimensional mechanics problems, but to canonical (Schroedinger) quantum field theories. I will discuss a range of examples from anharmonic oscillators to scalar field theory and Yang-Mills theory, as well as possible extensions to canonical quantum gravity.