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Added by Arxiv Bot | Added: 2026-03-02 18:01 | Views: 0 | Source: arXiv Dataset IDs (Model)

Reciprocal Symmetric and Origin of Quantum Statistics

Authors	Mushfiq Ahmad
Categories	physics.gen-ph
ArXiv ID	physics/0703194
URL	https://arxiv.org/abs/physics/0703194

Abstract

Boltzmann's differential equation is replaced by the corresponding reciprocal symmetric finite difference equation. Finite difference translates discreteness of energy. Boltzmann's function, then, splits into two reciprocally related functions. One of them gives Planck's radiation relation and the other one gives the corresponding Fermi-Dirac relation.

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    "abstract": "Boltzmann\u0027s differential equation is replaced by the corresponding reciprocal\nsymmetric finite difference equation. Finite difference translates discreteness\nof energy. Boltzmann\u0027s function, then, splits into two reciprocally related\nfunctions. One of them gives Planck\u0027s radiation relation and the other one\ngives the corresponding Fermi-Dirac relation.",
    "arxiv_id": "physics/0703194",
    "authors": [
      "Mushfiq Ahmad"
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    "categories": [
      "physics.gen-ph"
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    "title": "Reciprocal Symmetric and Origin of Quantum Statistics",
    "url": "https://arxiv.org/abs/physics/0703194"
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