573lec36

573lec36 - 5.73 Lecture #36 36 - 1 Read CTDL, pp. 1156-1178...

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36 - 1 5.73 Lecture #36 updated September 19, NEXT TIME :e in solids (CTDL, pages 1156-1168) LAST TIME : TODAY : Landé interval rule (assignment!) ζζ NLS n ,, () l examples evaluate matrix elements in Slater determinantal basis and in many-e |NJLSM J or |NLM L SM S basis 1. electrons vs. holes—a shortcut: (holes are a convenience in spectra of isolated atoms and molecules, but they are an essential part of the interpretive picture for solids) 2. Hund’s 3rd rule 3. Zeeman effect: Landé g-factor formula via W-E Theorem (done previously by projection theorem) 4. Matrix elements of H Zeeman in Slater determinantal basis set. No difference between electron and hole as far as Zeeman effect is concerned. er ij 2 vs. SO H Hs L S s SO (one for each L - S term) (one for entire configuration) = ⋅→ →⋅ i iii i n ii ar l l l off - diagonal J = 0 intraconfigurational matrix elements: See notes [page 35- 9]! SO = H H eg I H SO .. ? 1 6 3 6 Read CTDL, pp. 1156-1178
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36 - 2 5.73 Lecture #36 updated September 19, 1. relationship between configurations with N e vs. N “holes” for p 5 is it necessary to consider all 5 e ? is the sign flip just a coincidence? NO! TRICK: Hole is exactly equivalent to e (for identical LM L SM S or JLSM J ) except that the sign of its charge is reversed. * no effect on e 2 /r ij because 2 interacting particles have charge of the same sign (either both e or both hole), so e 2 /r ij is always a repulsive interaction . [What happens for f 13 p? Certainly different from fp!] * reverse sign for H SO because H SO is a relativistic electrostatic interaction between e and nucleus (+ charge). Replacing e by h + and leaving the sign on the nucleus the same reverses the sign of H SO ! subshell 1/ 2 full subshell s p d f # e 1 3 5 7 n N l () e.g. 1 1 0 0 1 (±1 is the unoccupied spin - orbital. It is the "hole") 1100 1 αβαβ α β ζα β α β α ζ −= = = === =− +− np P M M np P M M e LS SO n p i iz iz np 52 2 11 2 2 1 2 1 2 00 1 2 5 , / , / H ls h so expectation value of SO SO H H : , / 5 1 2 2 1 1 1 2 2 12 2 e np P M M e np n p z z np =+ ζ ζ h s l h but for single e (with the same M L , M S as the five e )
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573lec36 - 5.73 Lecture #36 36 - 1 Read CTDL, pp. 1156-1178...

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