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Equations with a self-consistent field in quantum-statistical theory of a crystal

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A system of equations with a self-consistent field is derived for the density of particles in the quantum case. This system has periodic solutions for a crystal. Equations for the Fourier coefficients are deduced from these solutions and are used to find equations containing only the Fourier coefficients of the density. A method is also given for solving the initial system by an expansion in powers of the Planck constant ħ; the terms proportional to ħ2 and ħ2 are calculated.

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Literature cited

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    I. P. Bazarov, Statistical Theory of the Crystal State [in Russian], Moscow State University (1972).

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    V. I. Zubov, Ann. Phys. (Leipzig),32, 93 (1975).

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    É. V. Gevorkyan, Teor. Mat. Fiz.,26, 282 (1976).

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    A. A. Vlasov, Many-Body Theory [in Russian], Gostekhizdat, Moscow (1950).

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    V. A. Golovko, Izv. Vyssh. Uchebn. Zaved. Fiz., No. 2, 67 (1979).

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 66–71, May, 1980.

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Golovko, V.A. Equations with a self-consistent field in quantum-statistical theory of a crystal. Soviet Physics Journal 23, 414–419 (1980). https://doi.org/10.1007/BF00891632

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  • Fourier
  • Periodic Solution
  • Fourier Coefficient
  • Initial System
  • Quantum Case