573lec37

573lec37 - 5.73 Lecture#37 Infinite 1-D Lattice CTDL pages 1156-1168 LAST TIME hole h vs e configurations l N 37 1 l2 2 l 1 N for N > 2l 1 NLS NLS

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
37 - 1 5.73 Lecture #37 updated September 19, 2003 @ 2:22 Infinite 1-D Lattice LAST TIME : TODAY : CTDL , pages 1156-1168 hole h vs. e configurations: for N > 2 +1 e unchanged unchanged +– 2 () →− [] + ll l l l NN ij n r NLS NLS 22 1 ζζ ζ Zeeman Effect Wigner-Eckart Theorem used to define g J Confirm by H Zeeman in Slater determinantal basis E Zeeman =−µ =+ + ++ −+ + 0 1 21 MgB g JJ SS LL JJz J next lecture equal spacings g J as L,S,J diagnostic 1 2 6 7 2 0 . cos .( ) ( ) . H as example of localization, delocalization, tunneling 2. secular equation for simplified 1- D lattice 3. eigenvectors by equal probability trick 4. restrict k to k : 1st Brillouin Zone 5. all of the allowed states? Bloch functions wavepackets,motion, group velocity 8. transitions – energy bands and intensity profiles 9. conductivity + =− = l l Ek E A k xe u x k ikx k ψ Hund’s 3rd Rule (Lowest L - S term of only) N < 2 +1 E for regular N = 2 +1 state: no fine structure N > 2 +1 E for inverted N MIN MIN l l l l l l JL S JLS J + + = + 211 2
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
37 - 2 5.73 Lecture #37 updated September 19, 2003 @ 2:22 R 2 + R 2 E n + 1 0 () E n 0 qualitative picture: atomic energy levels tunneling between identical localized states slow behind big barrier (small splitting) fast behind small barrier (large splitting) levels bands, of width related to tunneling rate Ra >> 0 and doubly degenerate for exact degeneracy, can choose any linear combination Localized basis set or Delocalized basis set localized left (0) right (0) delocalized left (0) right (0) ψψ ψ = [] 2 12 / E lowest =− 1 2 H 2 + Start with H a lattice with only 2 equivalent sites. 2 + , x 2 atoms 2 states
Background image of page 2
37 - 3 5.73 Lecture #37 updated September 19, 2003 @ 2:22 double degeneracy at R → ∞ If initially in localized state, tunneling rate depends on * height relative to E of barrier * width of barrier * size of overlap between exponential tails of and n (0) left (0) right (0) () ψψ clear that tunneling rate (i.e. splitting) increases
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/28/2011 for the course CHEM 5.74 taught by Professor Robertfield during the Spring '04 term at MIT.

Page1 / 9

573lec37 - 5.73 Lecture#37 Infinite 1-D Lattice CTDL pages 1156-1168 LAST TIME hole h vs e configurations l N 37 1 l2 2 l 1 N for N > 2l 1 NLS NLS

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online