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Electrons and Phonons
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absorption approximation assumed atomic axis band index band structure Bloch functions Brillouin zone calculation coefficient components conductivity constant contribution Coulomb crystal defined delta function denoted density dependence described determined diagonal diagrams dielectric function discussion effective mass electric field energy band evaluate exciton expression factor Fermi energy Fermi surface ferromagnetic finite Fourier transform free electron frequency given Green's function ground state energy Hamiltonian Hartree-Fock hole imaginary impurity integral introduce involving Landau levels lattice vector Let us consider limit magnetic field matrix element metal momentum neglected normal obtained operator optical orbit oscillations pairs parabolic band parameter particle perturbation theory phonon Phys potential present problem quantity quantum relation replace representation resonance result scattering second order second-order Section self-energy semiconductors simple single-particle solid solution substituted superconducting suppose symmetry temperature tensor tion transition vanishes Wannier functions wave function wave vector zero