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For example, the gradient of a differentiable function vanishes at local maxima
and minima, but the boundedness and periodicity of each S„(k) insure that for
each n there will be at least one maximum and minimum in each primitive cell.28
It therefore fails (in contrast to the free electron case, page 14) to approach 90° in
the high-field limit. high-field limit only if the projection of the electric field on n, E •
n, vanishes.43 The electric field therefore has the form (see Figure 12.11) E ...
8 Ions separated by Bravais lattice vectors have the same total charge, so e,
depends only on d, and not on R. * In deriving (27.18) wc have used the fact that
the total charge of the primitive cell. le(d), vanishes. We have also neglected an ...
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The Dmle Theory of Metals
The Sommerfeld Theory of Metals
Failures of the Free Electron Model
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alkali atomic band structure Bloch boundary condition Bragg plane Bravais lattice Brillouin zone calculation carrier densities Chapter coefficients collisions conduction band conduction electrons contribution crystal momentum crystal structure density of levels dependence described determined Drude effect electric field electron gas electron-electron electronic levels energy gap equilibrium example Fermi energy Fermi surface Figure frequency given Hamiltonian hexagonal holes impurity independent electron approximation insulators integral interaction ionic crystals ions lattice planes lattice point linear magnetic field metals motion nearly free electron neutron normal modes Note number of electrons one-electron levels orbits periodic potential perpendicular phonon Phys plane waves primitive cell primitive vectors problem properties quantum reciprocal lattice vector region result scattering Schrodinger equation semiclassical semiclassical equations semiclassical model semiconductors simple cubic solid solution specific heat sphere spin superconducting symmetry temperature term thermal tight-binding valence valence band vanishes velocity wave functions wave vector zero