Eur. Phys. J. D 65, 331-351 (2011)
https://doi.org/10.1140/epjd/e2011-20261-6

Regular Article

Classical approach in atomic physics

Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia

^a e-mail: esolovev@theor.jinr.ru

Received: 4 May 2011
Received in final form: 11 July 2011
Published online: 25 November 2011

Abstract

The application of a classical approach to various quantum problems – the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a semiclassical spectrum of a hydrogen atom in crossed electric and magnetic fields, a spontaneous decay of excited states of a hydrogen atom, Gutzwiller’s approach to Stark problem, long-lived excited states of a helium atom discovered with the help of Poincaré section, inelastic transitions in slow and fast electron-atom and ion-atom collisions – is reviewed. Further, a classical representation in quantum theory is discussed. In this representation the quantum states are treated as an ensemble of classical states. This approach opens the way to an accurate description of the initial and final states in classical trajectory Monte Carlo (CTMC) method and a purely classical explanation of tunneling phenomenon. The general aspects of the structure of the semiclassical series such as renormgroup symmetry, criterion of accuracy and so on are reviewed as well.