The Gutzwiller trace formula#
The exact one-dimensional Gutzwiller trace formula, reconstructing a spectrum purely from a single classical periodic orbit’s action and period, and the general isolated-orbit stability amplitude used beyond the exactly-solvable 1D case; the quartic oscillator’s spectrum and revivals; the Berry-Tabor length spectrum of an integrable billiard; Balian and Bloch’s smoothed level density of a billiard; and Bogomolny’s transfer operator, quantizing the disk and the stadium on their boundaries.
Balian and Bloch’s level-density expansion for billiards
Balian and Bloch's level-density expansion for billiards
The Berry-Tabor formula: an integrable billiard’s spectrum
The Berry-Tabor formula: an integrable billiard's spectrum
Bogomolny’s transfer operator: quantizing a billiard on its boundary
Bogomolny's transfer operator: quantizing a billiard on its boundary
Gutzwiller’s trace formula: a spectrum from classical orbits
Gutzwiller's trace formula: a spectrum from classical orbits
