The bulk modulus B of a solid is defined as: where V is the volume, P the pressure, and E the total energy; this quantity describes how the solids respond to external pressure by changes in volume. Show that for the uniform electron gas with kinetic energy and exchange energy terms only, Eqs (1.8) and (4.64), respectively, the bulk modulus is given by: or equivalently, in terms of the kinetic and exchange energies: Discuss the physical implications of this result for a hypothetical solid that might reasonably be described in terms of the uniform electron gas, and in which the value of (rs/a0) is relatively small [(rs/a0) < 1].
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