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Helium  - first part - Coordinates, approximations, Identical particles, spin - 16.09.2010
This is a system where we must consider 2 particles - at least
Center of mass is to high accuracy (4 times nearly 2000 ) at the nucleus
Can not be solved analytically at all
he_1.png

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Approximations; or models
First - switch off the REPULSION between the electrons
he_2.png
From the exam slides - we have seen only at the He, none of the ions

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Now we move to a different problem: in treating 2 electrons, and especially more than two,
new discoveries were made: the necessity of Aufbau principle
and the exclusion principle
These principles were replaced by a new concept - IDENTICAL PARTICLES
he_3.png

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The above guess can be instead of guessing be based on a mathematical technique - exchange operation
he_4.png

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Symmetric, antisymmetric - and trying to put two in the same state into the antisymmetric
leads to the reformulation of the exclusion principle
he_5.png

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When we have more than two particles
SLATER DETERMINANT ( essential in the many electron atoms theories )
he_6.png

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he_7.png
Homework - work with the determinants. work out the formula for three identical particles - using the determinant

Determinant is mathematical object incorporating the antisymmetry of exchanges - permutations
A similar, but little known SYMMETRICAL object is called "The permanent" see it defined at wikipedia
http://en.wikipedia.org/wiki/Permanent
Somebody has also written a nice story of the determinant - http://en.wikipedia.org/wiki/Determinant

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