Abstract
The homogeneous electron gas model has been quite successful to predict the bulk properties of systems of electrons at various densities. In many occasions, a simplified free homogeneous electron gas model represents a powerful first approximation to a real system. Despite our considerable knowledge on the bulk properties of a homogeneous electron gas, advances in nanoscience and nanotechnology call for a greater effort to understand the opposite limit of small finite systems of electrons with size-dependent properties. In this work, we provide a detailed description of the properties of a finite fully spin-polarized (spinless) free homogeneous one-dimensional electron gas, the simplest of the free homogeneous electron gases. We derive exact analytical results for various quantities such as the one-particle density function, two-particle density function, one-particle density matrix, pair correlation function and energy of finite systems with an arbitrary number of electrons. The results obtained provide a detailed view on how various quantities corresponding to a finite system approach their bulk (thermodynamic limit) value.
Highlights
The theoretical description of Fermi systems, typically systems of electrons, has been the subject of many studies and has a long history.[1,2,3,4,5] Real systems of many electrons involve interactions and can be treated only by adopting models and approximations that attempt to solve the many-particle Schrödinger’s equation as accurately as possible
IV we describe in detail the calculations of the one-particle density matrix function and pair correlation function for a finite system with an arbitrary odd number (N = 1, 3, . . .) of electrons
In this work we studied the properties of a finite fully spin-polarized free 1DEG consisting of an arbitrary number of electrons
Summary
The theoretical description of Fermi systems, typically systems of electrons, has been the subject of many studies and has a long history.[1,2,3,4,5] Real systems of many electrons involve interactions and can be treated only by adopting models and approximations that attempt to solve the many-particle Schrödinger’s equation as accurately as possible. In all other regards they manifest quantum behavior (they obey Pauli’s exclusion principle, and so on) From this perspective, a free electron gas model represents a quantum system of interaction-free electrons with the constrain that the particles should abide by the laws of quantum mechanics. In this work we derive exact analytic expressions for all relevant quantities (one-particle density matrix, pair correlation function, energy, etc) that correspond to a finite fully spin-polarized (spinless) free homogeneous 1DEG system of N electrons as a function of the arbitrary number of electrons. VII we draw some conclusions and present a brief summary of the results
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