Quantum 115B

Quantum 115B

1. 1st MT

2. 2nd MT

3. New: Ch. 5&6

   • 2 Particle Systems
     • Indistinguishable
       • Symmetric
         • Bosons
           • photons, mesons
           • integer spins
           • Total Wavefunction: Same as Slater Det. but with pluses
       • Anti-Symmetric
         • Slater Determinant
           • Ya(x1) Yb(x1) Yc(x1) Ya(x2)Yb(x2)Yc(x2) Ya(x3)Yb(x3)Yc(x3)
             • X's stay the same across A's stay the same down
             • A = 1/Sqrt[n!]
         • Fermions
           • electrons, protons
           • half integer spins
           • *identical fermions cannot occupy the same state!
     • Distinguishable, Classical
       • Multiply Wavefunctions, add energies
   • Atoms
     • Parahelium/Orthohelium
     • Periodic Table
       • H= (1s) He= (1s)^2
       • Totals: L=
   • Solids
     • Free Electron Gas
       • Fermi Energy
         • Each pair of electrons occupies a volume of: 1/8 sphere or 1/4 circle
           • Solve for Kf
             • plug in electron density (rho or sigma)
               • 3D: rho = Nq/V
               • Plug Kf into E
                 • Efermi= h^2/2m (3 rho pi^2)^2/3
               • 2D: Sigma = Nq/A
       • Density of states
         • N(E)
       • Sommerfield: Model which treats all electrons in a metal like Free Particles in a 3D box
         • *3D analog to the infinite square well
           • En= (h^2 pi^2 /2ml) (nx^2 + ny^2 +nz^2)
   • Stat. Mech.
     • Maxwell Boltzmann
       • n(E)= A exp[-(E-mu)Beta]
     • Fermi-Dirac
       • n(E)= 1/ [exp(E-mu)Beta+1]
         • Difference is the PLUS
     • Bose-Einstein
       • n(E)=1/ [exp(E-mu)Beta-1]
         • Difference is the MINUS
     • Configurations
       • Ex. Three particles, Occupation #'s: n1=1, n2=1, n3=1
         • Config. = (0,3,0,0,..)
     • Totals
       • Total # of Particles = N = Int. D(E) n(E,T) dE
         • Total Energy in system= E = Int. E D(E) n(E) dE
   • Non-Degenerate Perturbation
     • First order Energy
     • First order Wavefunction
     • Second order energy

4. REAL old stuff

   • Infinte Square well
     • En= n^2 pi^2 h^2 2ma^2
     • Psi(x)= Sqrt(2/a) Sin[n pi x/a]
   • Harmonic Oscillator
     • Ladder Method
       • Raising: a+Yn = Sqrt[n+1] Yn+1 Lowering: a-Yn = Sqrt[n] Yn-1
         • x=Sqrt[h/2mw](a+ + a-) p=iSqrt[hmw/2](a+ - a-)
     • Analytic Method
       • Hermite Polynomials
   • Free Particle