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hw8_f10 - Physics 112 Fall 2010 Holzapfel Problem Set 8(6...

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Physics 112, Fall 2010: Holzapfel Problem Set 8 (6 Problems). Due Monday November 1, 5 PM Problem 1 : Density of orbitals in one and two dimensions Kittel 7.1 Problem 2 : Energy of a Relativistic Fermi Gas Kittel 7.2 Problem 3 : Liquid 3 He as a Fermi gas Kittel 7.5 Problem 4 : Relativistic White Dwarf Stars Kittel 7.10 Problem 5 : Magnetic Susceptibility of a Fermi Gas An ideal gas of N spin 1/2 fermions is constrained in a volume V. A small, constant magnetic induction field B = μ 0 H is applied along the direction so that the energies are ε = ¯ h 2 k 2 2 m ± μ B B with the minus sign if the spins are parallel to the field. a) Show that the magnetic susceptibility is χ = M H = μ 0 μ 2 B D ( ε F ) V where D ( ε F ) is the density of states in energy at the Fermi level. b) Use the fact that D ( ε ) V ε to estimate χ for copper, given that ε F = 7 . 0eV and the density of free electrons is n = 8 . 5 × 10 28 m - 3 . Problem 6 : Corrections to ideal gas behavior
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