Complex sentence: He was also the first to investigate the relationship between classical and quantum mechanics in chaotic systems; he developed the Gutzwiller trace formula, the main result of periodic orbit theory giving a recipe for computing spectra from periodic orbits of a system.
Split into simpler sentences: 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.