Study of the Features and Properties of Greens Functions of Macroscopic Quantum Systems

Abstract

This article is devoted to the theoretical investigation of processes in macroscopic systems based on wave particle duality and quantum statistical distributions using the Green’s function method. In particular, it pro vides a detailed description of the properties and characteristics of the Green’s function for an ideal Fermi liquid, single- and two-particle Green’s functions, as well as Green’s functions at limiting temperatures and for the Dirac and Schrödinger equations. The study analyzes the application of the Green’s function method to processes in many-particle quantum systems and to solving equations that describe the constituent particles of such systems. For a given operator and set of boundary conditions, a Green’s function can be defined, al lowing the solution of the corresponding equation to be expressed in integral form. A distinctive feature of this method is the application of mathematical-physics tools, such as Fourier methods, integral transforms, special functions, and mathematical analysis, to problems in quantum physics governed by the principles of quantum and statistical mechanics. The relevance of this study stems from the application of the Green’s function method to the analysis of quantum phenomena. This approach is considered one of the effective methods for solving partial differential equations describing various physical processes. It involves transform ing the original differential equation into an equivalent integral equation involving Green’s functions, which can then be solved. The transformation involves passing to the momentum representation and applying Fouri er transforms using methods of complex analysis.