Study of Сollision of Two Solid Point Particles in the Formalism of Quantum Mechanics in Phase Space

The study of the relation between quantum and classical paradigms of description of physical systems is one of the fundamental problems of modern theoretical physics. This paper presents a comprehensive analysis of this problem on the example of a simple model system - the process of interaction of two colliding particles. A wide range of theoretical approaches is considered, including the formalism of quantum mechanics in the Schrödinger and Heisenberg representations, quasi-classical methods such as the WCB approximation, the use of the Wigner function to visualize quantum effects in phase space, and numerical simulation of the dynamics through the calculation of the temporal evolution of correlation functions. Special emphasis is placed on the visualization and interpretation of specific quantum effects, such as entanglement and coherence, in terms of the Wigner function in phase space. An overview of current research in this area is given, covering the phenomena of quantum-classical correspondence breaking, dynamical generation of entanglement, coupling of quantum and classical work distributions, and the influence of various factors - external fields, multiparticle interactions, and others. A mathematical formalism for modeling the Wigner function with respect to coherent and compressed quantum states is presented. The work makes a significant contribution to the fundamental understanding of the limits of applicability of quantum and classical descriptions and related phenomena at the junction of the two paradigms.