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PARTICLE PLACEMENT IN AN ATOM BASED ON THE FERMI-DIRAC AND BOSE-EINSTEIN DISTRIBUTION ACCORDING TO THE VALUE OF THE SPIN QUANTUM NUMBER

K.A. Nurullayev J.N. Xoʻjamberdiyeva

Published Apr 1, 2026• 0 citations
Publisher

Abstract

The article discusses the significance of the arrangement of atoms and molecules in a substance that forms stable systems, such as an atom and a molecule. It examines the patterns of combining elementary particles, such as electrons and nuclei, which are present in nature, to form atoms, as well as their distribution within an atom. The article provides information about the differences in elementary particles, which have been verified by scientists, based on their spin values, and how they follow different distributions based on their spin values, as well as their arrangement within an atom based on the Pauli principle. The Fermi-Dirac and Bose-Einstein distributions are the fundamental concepts of atomic and molecular physics and provide a complete answer to the question of whether the system and the physical properties of a molecule or an atom depend on the arrangement of the elementary particles that make up the system.

DOI
10.5281/zenodo.19364333

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The article discusses the significance of the arrangement of atoms and molecules in a substance that forms stable systems, such as an atom and a molecule. It examines the patterns of combining elementary particles, such as electrons and nuclei, which are present in nature, to form atoms, as well as their distribution within an atom. The article provides information about the differences in elementary particles, which have been verified by scientists, based on their spin values, and how they follow different distributions based on their spin values, as well as their arrangement within an atom based on the Pauli principle. The Fermi-Dirac and Bose-Einstein distributions are the fundamental concepts of atomic and molecular physics and provide a complete answer to the question of whether the system and the physical properties of a molecule or an atom depend on the arrangement of the elementary particles that make up the system.
INDIVIDUALAtomism in its latest form is called quantum mechanics.It has extended its range to comprise, besides ordinary matter, all kinds of radiation, including light-in brief, all forms of energy, ordinary matter being one of them.In the present form of the theoiy the "atoms" are electrons, jorotons, photons, mesons, etc.The generic name is elementary particle, or merely particle.The term "atom" has very wisely been retained for chemical atoms, though it has become a misnomer.This essay deals with the elementary particle, more particularly with a certain feature that this concept has acquired-or rather lost in quantum mechanics.I menn this : That the elementary particle is not an individual; it cannot be identified, it lacks "sameness."The fact is known to every physicist, but is rarely given any prominence in surveys readable by nonspccialists.In technical language it is covered by saying that the particles "obey" new-fangled statistics, either Einstein-Bose or Fermi-Dirac statistics.The implication, far from obvious, is that the unsuspected epithet "this" is not quite prop- erly applicable to, say, an electron, except with caution, in a restricted sense, and sometimes not at all.My objective here is to explain this point and to give it the thought it deserves.In order to create a foil for the discussion, let me summarize in sections 2-5 what we are usually told about particles and waves in the new physics.2. CURRENT VIEWS: THE AMALGAMATION OF PARTICLES AND WAVES Our image of the material world had been made up of two kinds of "fittings"-waves and particles.The former were instanced mainly, if not exclusively, by Maxwell's waves of electromagnetic energy, comprising such as are used in radio, light, X-rays, and gamma-rays.Material bodies were said to consist of particles.One
With the advent of general relativity and quantum mechanics, physics has in many cases shifted the emphasis from dynamics to symmetry principles associated with different types of mathematical groups. We speak of the group structure of crystals, the group invariants of the equations of motion, the group classification of elementary particles, and also of the group homeomorphisms of fractals. The objective of this article is to show how the group theoretical structure of entanglement can be used to classify atomic and molecular structure. The article begins by establishing a working definition of entanglement and then using it to derive the Pauli-exclusion principle by showing that Fermi-Dirac statistics can be considered as an entangled state invariant under the action of the SL(n, C)With the advent of general relativity and quantum mechanics, physics has in many cases shifted the emphasis from dynamics to symmetry principles associated with different types of mathematical groups. We speak of the group structure of crystals, the group invariants of the equations of motion, the group classification of elementary particles, and also of the group homeomorphisms of fractals. The objective of this article is to show how the group theoretical structure of entanglement can be used to classify atomic and molecular structure. The article begins by establishing a working definition of entanglement and then using it to derive the Pauli-exclusion principle by showing that Fermi-Dirac statistics can be considered as an entangled state invariant under the action of the SL(n,C)SL(n, C)SL(n,C) group. Based on this, a group classification scheme of entangled states is proposed to distinguish atomic and molecular structures associated with chemical bonds. group. Based on this, a group classification scheme of entangled states is proposed to distinguish atomic and molecular structures associated with chemical bonds.
Synopsis: The connection between a particle’s spin and the statistics it obeys is given. Bose–Einstein and Fermi–Dirac statistics are explained and illustrated with products of wave functions. A new type of particle basis state is described, and two possibilities for the commutation properties of the associated raising (“creation”) and lowering (“annihilation”) ladder operators are examined, giving rise to the Bose–Einstein and Fermi–Dirac cases. The relation between particle occupation number and energy is inferred from detailed balance, and cubical enclosures of particles are studied. Two physics mysteries encountered in the earlier chapters (zweideutigkeit and the vanishing electronic component of specific heat) are explained. The Hartree–Fock theoretical framework for the approximate treatment of many-particle atomic systems is constructed.
Synopsis: ƒe connection between a particle’s spin and the statistics it obeys is given. Bose-Einstein and Fermi-Dirac statistics are explained and illustrated with products of wave functions. A new type of particle basis state is described and two possibilities for the commutation properties of the associated raising (“creation”) and lowering (“annihilation”) ladder operators are examined, giving rise to the Bose-Einstein and Fermi-Dirac cases. ƒe relation between particle occupation number and energy is inferred from detailed balance, and cubical enclosures of particles are studied. Two physics mysteries encountered in the earlier chapters (“zweideutigkeit” and the vanishing electronic component of specific heat) are explained. ƒe Hartree-Fock theoretical framework for the approximate treatment of many-particle atomic systems is constructed.