Gutzwiller formulated the
Gutzwiller approximation for describing electrons with strong local interactions in terms of the Gutzwiller wave function, composed of a simple many-electron wave function acted on by a correlation operator ("Gutzwiller projection"). He was also the first to investigate the relationship between classical and quantum mechanics in chaotic systems. In that context, he developed the Gutzwiller trace formula, the main result of periodic orbit theory, which gives a recipe for computing spectra from periodic orbits of a system. He is the author of the classic monograph on the subject,
Chaos in Classical and Quantum Mechanics (1990). Gutzwiller is also known for finding novel solutions to mathematical problems in field theory, wave propagation, crystal physics, and celestial mechanics. In appreciation of his contributions to theoretical physics, the
Max Planck Institute for the Physics of Complex Systems (MPIPKS) annually awards the Martin Gutzwiller Fellowship to acknowledge and promote exceptional research in this field. ==Book collecting==