Week 6 Free Electron Model Flashcards
how does EM radiation work with regards to optical and acoustic
only optical modes are coupled to photons
what assumptions can be made for the free-electron model
assume lots of electrons so that you could ignore interactions between valence electrons and atoms
what are three steps for the QM approach for the model
find energy spectrum of a single electron
use build up principle to obtain total energy
include fermi electrons
when is a periodic boundary condition applied
when L is macroscopic
what is the PBC energy continuum band
E(k) = ħ^2k^2/2m = ħ/2mL^2 (nx^2 + ny^2 + nz^2)
what is the wave function of a PBC electron
ψ = Aexp[i(k*r)]
what is k-space
states are just points in k-space
what is the 3D volume of a single state
8π^3/V
what is the number of states per volume equation
dn = 2k^2dk/2π^2
define density of states
number of states per unit volume with energy E in interval E to E+dE
what does the ground state give
Fermi momentum, Fermi energy, Fermi temperature
give the Fermi momentum, energy and temperature equation
Pf = mv_f = ħk_f Ef = ħ^2k^2 / 2m Tf = Ef / k
how does energy relate to electron density
energy rapidly increases as electron density increases
