Classical approach in quantum physics

TL;DR

This paper reviews classical methods applied to quantum problems, exploring semiclassical approaches, classical representations in quantum theory, and their implications for understanding quantum phenomena through classical analogs.

Contribution

It discusses the application of classical approaches to quantum problems and introduces a classical representation in quantum theory, enhancing the understanding of quantum states and phenomena.

Findings

Classical methods effectively describe certain quantum systems.

Classical representation aids in understanding tunneling and state transitions.

Semiclassical series and their accuracy criteria are reviewed.

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 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 recently discovered with the help of Poincar$\acute{\mathrm{e}}$ 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 treating 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. In conclusion, the relation between quantum theory, classical physics and measurement is discussed.