Quantum Oscillator at Temperature <i>T</i> and the Evolution of a Charged-Particle State in the Electric Field in the Probability Representation of Quantum Mechanics

• Published in: Entropy
• Main Authors: Margarita A. Man’ko, Vladimir I. Man’ko
• Format: Article
• Language: English
• Published: MDPI AG 2023-01-01
• Subjects: tomographic probability distribution; integrals of motion; coherent state; normal probability distribution; entropy
• Online Access: https://www.mdpi.com/1099-4300/25/2/213
• ISSN: 1099-4300

A short review constructing the probability representation of quantum mechanics is given, and examples of the probability distributions describing the states of quantum oscillator at temperature <i>T</i> and the evolution of quantum states of a charged particle moving in the electric field of an electrical capacitor are considered. Explicit forms of time-dependent integrals of motion, linear in the position and momentum, are used to obtain varying probability distributions describing the evolving states of the charged particle. Entropies corresponding to the probability distributions of initial coherent states of the charged particle are discussed. The relation of the Feynman path integral to the probability representation of quantum mechanics is established.