Lecture10-06.1-Ideal_Gas-Fermions-Bosons

Lecture10-06.1-Ideal_Gas-Fermions-Bosons - 1 Last Time...

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Unformatted text preview: 1 Last Time Gibbs Factor (Boltzmann factor with N) Gibbs Sum (Partition function with N) Adsorption (O 2- myoglobin ) Semiconductor Impurity Sites LECTURE 10 Today Chapter 6 (part 1) Ideal Gas: Fermions and Bosons Fermions and bosons Fermi-Dirac Distribution (fermions) Bose-Einstein Distribution (bosons) Density of states LECTURE 10 2 Matter No two pieces of matter may occupy the same space at the same time Half-true… Two kinds of particles Fermions (spin 1/2, 3/2, 5/2, etc.) • Cannot occupy the same state at the same time • Pauli exclusion principle Antisocial Bosons (spin 0, 1, 2, etc.) • Can occupy the same state at the same time All Follow the Crowd The difference between a gas of fermions and a gas of bosons becomes apparent at low temperature. 3 Electrons are Fermions Pauli exclusion principle Why most matter cannot occupy the same space at the same time O n l y O n e F e r m i o n A l l o w e d Bosons Can occupy the same space at the same time Photons are bosons b lasers Helium is a boson b superfluidity 4 Orbitals Thermal average occupancy f ( ε , τ , μ ) distribution function Orbital: a state of Schrödinger equation for one particle For weak interaction: approximate exact quantum state of a system by assigning particles to orbitals, each being a solution of single particle Schrödinger equation Different f for fermions and bosons 1 or 0 particles on each orbital Any number of particles on each orbital Different Gibbs Sums for each orbital f ( ε , τ , μ )<<1: distribution for fermions and bosons should be similar Fermions Only two terms for a single fermion state Average occupancy of the orbital Fermi-Dirac Distribution Function O n l y O n e F e r m...
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This note was uploaded on 12/14/2010 for the course PHYSICS 416 taught by Professor Savikhin during the Spring '10 term at Purdue.

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Lecture10-06.1-Ideal_Gas-Fermions-Bosons - 1 Last Time...

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