Semiclassical Descriptions of Quantum Mechanics

William Hughes Miller

William Hallowes Miller

S. P. Misra, T. S. Shankara

In the semiclassical descriptions, it is usual to describe a quantum-mechanical system in a classical language with (i) a correspondence between classical functions and operators of quantum mechanics and (ii) with a real, but not necessarily positive, probability density function in phase space corresponding to a particular quantum-mechanical state. The general forms of such semiclassical descriptions is discussed. The conditions for the two descriptions to be equivalent are also examined.

Regina Maria Ricotta

Guillermo Chacón‐Acosta, Héctor H. Hernández

We study the Hydrogen atom as a quantum mechanical system with a Coulomb like potential, with a semiclassical approach based on an effective description of quantum mechanics. This treatment allows us to describe the quantum state of the system as a system of infinite many classical equations for expectation values of configuration variables, their moments and quantum dispersions. It also provides a semiclassical description of the orbits and the evolution of observables and spreadings and their back-reaction on the evolution.