Free electron gas Handout

Free electron gas Handout - University of California,...

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- 35 - University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor Free Electron Gas (Read Kittel Ch. 6) Assume non-interacting particles, mass m, spin 1/2, in a 3-D box periodic boundary conditions: etc. for y,z. plane wave solutions. energy (dispersion relation) momentum velocity Mode counting Each state (mode) occupies volume in k-space. Total # of states N, with wavevector k : total # states N, with energy is: L L L Volume V = L 3 ψ r () Ae ik r = N 2 4 π 3 ------ k 3 2 π L ⎝⎠ ⎛⎞ 3 -------------- V 3 π 2 -------- k 3 == spin E
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- 36 - University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor Density of states Occupation of states We have to do quantum statistical mechanics. Classical , distinguishable particles can have any # of particles in any state. Classical phys- ics has no restrictions. Classical particles can be shown to satisfy a Maxwell-Boltzman dis- tribution - probability of occupation of state at energy, E: Quantum mechanics - identical particles are indistinguishable. Hamiltonian invari- ant on interchange of any two particles wave function symmetric or antisymmetric on particle interchange.
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This note was uploaded on 08/01/2008 for the course EE 230 taught by Professor Bokor during the Spring '08 term at Berkeley.

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Free electron gas Handout - University of California,...

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