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absolute zero alloys approximation atoms band edge Bloch Brillouin zone calculated Chapter charge collisions components conduction band conduction electrons crystal structure deﬁned density dielectric constant dielectric function diffraction direction dislocation dispersion relation displacement effective mass elastic electric ﬁeld electron concentration electron gas energy band energy gap equation equilibrium exciton experimental Fermi surface ferromagnetic Figure ﬁlled ﬁlm ﬁnd ﬁrst Brillouin zone Fourier free atom free electron frequency germanium heat capacity hole impurity integral interaction ion cores lattice constant lattice point low temperatures magnetic ﬁeld metals modes momentum motion nearest-neighbor normal optical orbitals oscillator particle phase phonon plane plasmons polarization positive potential energy primitive cell quantum reciprocal lattice vector reﬂection region resonance result scattering semiconductor shown in Fig silicon Solid state physics space specimen sphere spin superconducting theory thermal tion transition unit valence band values velocity volume wave wavefunction wavelength wavevector zone boundary zone scheme