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