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