## Solid State PhysicsThis book provides an introduction to the field of solid state physics for undergraduate students in physics, chemistry, engineering, and materials science. |

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Page 35

The

of the electron's spin along an arbitrary axis, which can take either of the two

values ft/2 or —h/2. Therefore associated with each allowed wave vector k are

two electronic levels, one for each direction of the electron's spin. Thus in

building up the N-electron ground state we begin by placing two electrons in the

. We then ...

The

**one**-**electron levels**are specified by the wave vectors k and by the projectionof the electron's spin along an arbitrary axis, which can take either of the two

values ft/2 or —h/2. Therefore associated with each allowed wave vector k are

two electronic levels, one for each direction of the electron's spin. Thus in

building up the N-electron ground state we begin by placing two electrons in the

**one**-**electron level**k = 0, which has the lowest possible one-electron energy 8 = 0. We then ...

Page 40

(2.39) We can therefore write (2.38) more compactly as: PN(E) = e-^-FN),kBT (

2.40) Because of the exclusion principle, to construct an iV-electron state one

must fill N different

be specified by listing which of the N

very useful quantity to know is/-*, the probability of there being an electron in the

particular

equilibrium.17 ...

(2.39) We can therefore write (2.38) more compactly as: PN(E) = e-^-FN),kBT (

2.40) Because of the exclusion principle, to construct an iV-electron state one

must fill N different

**one**-**electron levels**. Thus each N-electron stationary state canbe specified by listing which of the N

**one**-**electron levels**are filled in that state. Avery useful quantity to know is/-*, the probability of there being an electron in the

particular

**one**-**electron level**i, when the N-electron system is in thermalequilibrium.17 ...

Page 41

allowed by the exclusion principle) we could equally well write (2.41) as (

summation over all N-electron ft" = 1 - £ PN(EyN) states y in which there is no

elec- (2.42) tron in the

in which there is an electron in the

electron state in which there is no electron in the level i, by simply removing the

electron in the ith level, leaving the occupation of all the other levels unaltered.

Furthermore ...

allowed by the exclusion principle) we could equally well write (2.41) as (

summation over all N-electron ft" = 1 - £ PN(EyN) states y in which there is no

elec- (2.42) tron in the

**one**-**electron level**i). 2. By taking any (N + l)-electron statein which there is an electron in the

**one**-**electron level**i, we can construct an JV-electron state in which there is no electron in the level i, by simply removing the

electron in the ith level, leaving the occupation of all the other levels unaltered.

Furthermore ...

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### Contents

The Drude Theory of Metals | 1 |

The Sommerfeld Theory of Metals | 29 |

Failures of the Free Electron Model | 57 |

Copyright | |

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### Common terms and phrases

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 direction Drude effect electric field electron gas electron-electron electronic levels energy gap equilibrium example face-centered cubic Fermi energy Fermi surface Figure free electron theory frequency given Hamiltonian hexagonal holes impurity independent electron approximation insulators integral interaction ionic crystals 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 vanishes velocity wave functions wave vector zero