Beyond quantum mechanics: Insights from the work of Martin Gutzwiller

A complete quantum solution provides all possible knowledge of a system, wh ereas semiclassical theory provides at best approximate solutions in a limi ted region. Nevertheless, semiclassical methods based on the work of Martin Gutzwiller can provide stunning physical insights in regimes where quantum solutions are Opaque. Furthermore, they can provide a unique bridge betwee n the quantum and classical worlds. We illustrate these ideas with an accou nt of a theoretical and experimental attack on the paradigm problem of the hydrogen atom in strong magnetic and electric fields.