Oks E. Analytical Advances in Quantum and Celestial Mechanics: Separating rapid and slow subsystems

IOP Publishing Ltd, 2020. — 145 p. — ISBN 978-0-7503-2510-3.Real physical systems very rarely allow exact analytical solutions of the equations describing the systems. Therefore, mathematicians and theoretical physicists over the last several centuries invented a variety of approximate analytical methods. Especially important are the methods going beyond the perturbation theory, such as, e.g., the method based on the separation of rapid and slow subsystems.
The latter method relates to systems consisting of two subsystems 1 and 2, where the characteristic time of the evolution of subsystem 1 is much smaller than the characteristic time of the evolution of subsystem 2. The two subsystems can interact very strongly, so that their interaction cannot be taken into account by the perturbation theory. In distinction, the method based on the separation of rapid and slow subsystems can provide an approximate analytical solution regardless of the strength of the interaction of the two subsystems.Quantum hydrogenic atoms or ions in a high-frequency laser field
Classical (Rydberg) hydrogen atoms in a high-frequency laser field: celestial analogies
Rydberg states of muonic-electronic helium atoms or helium-like ions
A circumbinary planet around a binary star in Einstein’s general relativity and in Newton’s gravity
Particular analytical solution for the unrestricted three-body problem of celestial mechanics: a ‘corkscrew’ orbit of a planet around a binary star or of a moon around a star-planet system
Magnetic stabilization of one-electron Rydberg quasimolecules
One-electron Rydberg quasimolecules in a high-frequency laser field
Quantum rotator-dipole in a high-frequency monochromatic field: a violation of the gauge invariance caused by the constraint
Center-of-mass effects for hydrogen atoms in a non-uniform electric field: applications to magnetic fusion, radiofrequency discharges, and flare stars
Advanced treatment of the Stark broadening of hydrogen spectral lines by plasma electrons
Advanced treatment of the Stark broadening of hydrogen-like spectral lines by plasma electrons
Concluding remarksAppendices
General analytical treatment of quantum systems in a high-frequency field
Analytical solution for Rydberg states of muonic-electronic negative hydrogen ion
An alternative analytical solution for Rydberg states of muonic–electronic helium-like atoms or ions