Closed-orbit theory

A semiclassical method that connects atomic spectra and photoabsorption in external fields to classical electron trajectories that leave and return to the nucleus.

Connect

Semiclassical approximation: An approximation that describes quantum systems using classical dynamics corrected by quantum phases and amplitudes. Closed-orbit theory applies this approximation to electrons moving in external fields.
Rydberg atom: An atom with an electron excited to a state of very high principal quantum number. Its loosely bound electron is especially sensitive to external fields and nearly classical motion.
Hydrogen atom in a magnetic field: The hydrogen atom whose electron dynamics are modified by an applied magnetic field. This canonical system exhibits recurring classical trajectories that imprint clear spectral structure.
Martin Gutzwiller: A physicist who developed a semiclassical trace formula connecting quantum spectra with classical periodic orbits. His periodic-orbit framework supplied a major conceptual precursor to closed-orbit methods.
Stationary-phase approximation: An asymptotic method that estimates oscillatory integrals from points where the phase is stationary. It selects classical trajectories whose contributions survive in the semiclassical signal.
Stark effect: The shift and splitting of atomic energy levels caused by an electric field. The field deforms the Coulomb dynamics and creates the trajectories analyzed by the theory.
Hydrogen atom in an electric field: The hydrogen atom subject to an external electric field that perturbs its Coulomb-bound electron. Its field-dependent photoabsorption provides a direct setting for closed-orbit calculations.
Michael C. G. H. T. G. Delande: A physicist known for theoretical work on quantum chaos and atoms in external fields. His research helped develop semiclassical descriptions of field-driven atomic spectra.
Semiclassical propagator: An approximation to quantum time evolution built from classical trajectories and their action, stability, and phase. Its trajectory contributions provide the amplitudes and phases used to construct closed-orbit signals.
Zeeman effect: The splitting or shifting of atomic energy levels in a magnetic field. Magnetic fields reshape electron motion and generate closed orbits with distinct actions.