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The Thomas-Fermi model provides a semiclassical approximation to describe the distribution of electrons in an atom, or more generally, in a system of many electrons. It treats the electron density as a continuous function rather than dealing with individual electrons explicitly. This model can also be applied to a system of N electrons confined in a cubic box of side (L), allowing us to estimate quantities like the total kinetic energy and the resulting pressure. In the Thomas-Fermi method, we consider electrons as forming a degenerate Fermi gas at zero temperature. The electrons occupy all quantum states up to the Fermi energy (E_F). In momentum space, the allowed states form a sphere of radius (p_F), the Fermi momentum. For a system of (N) electrons confined in a cubic box of volume (V = L^3), the number of electrons is related to the density of states in momentum space. In three dimensions, each quantum state occupies a volume (h^3) in phase space, and the number _________ ___ __________ ________ __________ _______ _______.
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