385lec28 - PHYS 385 Lecture 28 Addition of angular momentum...

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PHYS 385 Lecture 28 - Addition of angular momentum 28 - 1 ©2003 by David Boal, Simon Fraser University. All rights reserved; further copying or resale is strictly prohibited. Lecture 28 - Addition of angular momentum What's important : atoms with many electrons addition of angular momentum Text : Gasiorowicz, Chap. 19 Atoms with many electrons Most atoms of chemical interest have more than the two electrons which we have discussed in the helium atom. The general Hamiltonian for the n electron system (neglecting spin interactions) is: H = -( h 2 /2 m e ) Σ i i 2 - Σ i Zke 2 / r Ni + Σ i j ke 2 / r ij . If the two electron problem was impossible to solve analytically, then certainly the n - electron problem is. So we proceed as before to decouple the interactions by introducing an effective charge Z' . Now, in the many-electron system this really is a dicey move because the effective change “seen” by an electron will depend on how many other electrons there are close to the nucleus. Hence, Z' = Z' ( n ). We won t let this bother us. So the Hamiltonian is separable as before: H 0 = i h 0 ( i ) and the wavefunction is a product of hydrogen-like basis states ψ tpt = φ 1s · · · φ (times spin factors) The “state” of the many electron system is the product of single electron “orbitals” φ .
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