Pauli Exclusion Principal

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Pauli Exclusion Principal Multi-electron Atom
Spin Operations Energy of He Excited
States Energy Difference for 2s and 2p orbitals
for Multi-electron Atoms
F. Grieman
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Pauli Exclusion Principle (not chem 1 version) ?
?space ?spin product function, space
spin coordinates Electrons probabilities not
exact trajectories they are
indistinguishable!!! How must our wave functions
indicate this? Permutation operator (i,j)
exchanges electrons i j Now (i,j) ??
must ?? 2 possibilities (i,j) ? ?
or (i,j) ? -?
symmetric antisymetric
Bosons Fermions
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Apply to He atom (first ground state X 1So)
(1,2) 1s(1) 1s(2) a(1) a(2) 1s(2) 1s(1)
a(2) a(1) (1,2) 1s(1) 1s(2) a(1) ß(2)
1s(2) 1s(1) a(2) ß(1) What to do??? Use
linear combination ? 1s(1)1s(2) (2)½/2
?(1)?(2) ?(1)?(2) (1,2) ? ?
(1,2) ?- -?- Slater Determinant
1sa 1sß 1 1sa(1) 1sß(1)

1sa(1)1sß(2) - 1sß(1)1sa(2) 2 1sa(2)
1sß(2)
1s(1)1s(2) ?(1)?(2) - ?(1)?(2)
x
x
x
OK
spin-orbital
electron
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He excited states 1So 3S1 ?space
1s(1)2s(2) no good! distinguished
electrons ? (2)½/2 1s(1) 2s(2) 2s(1)
1s(2) ?spin a(1)a(2)
ß(1)ß(2) ß(1)a(2)
a(1)ß(2) ?total ?space ?spin Allowed
Wavefunctions ? (2)½/2 ?(1)?(2) -
?(1)?(2)
a(1)a(2)
?- (2)½/2 ?(1)?(2)
?(1)?(2)
ß(1)ß(2)
ok
ok
symmetric antisymmetric
x
(2)½/2 ?(1)?(2) ?(1)?(2) (2)½/2 ?(1)?(2)
- ?(1)?(2)
x
x
sym sym sym anti anti sym anti anti
ok
ok
x
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Example of Spin Operations on He excited state
1s(1)2s(2) configuration ? (2)½/2
1s(1)2s(2) 2s(1)1s(2) ?(1So) ? (2)½/2
?(1)?(2) - ?(1)?(2) ?? ?? - ??
?(1)?(2)
?? ?(3S1) ?- (2)½/2 ?(1)?(2)
?(1)?(2) ?? ??
?(1)?(2)
?? Spin Operations on 1So
Sz (2)½/2 ?(1)?(2) - ?(1)?(2)
(0) (2)½/2 ?(1)?(2) - ?(1)?(2)

S2 (2)½/2 ?(1)?(2) - ?(1)?(2)
(0) (2)½/2 ?(1)?(2) - ?(1)?(2)
S 0 Ms 0
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Spin Operations on 3S1
?(1)?(2)
(1) ?(1)?(2) Sz
(2)½/2 ?(1)?(2) ?(1)?(2) (0)
(2)½/2 ?(1)?(2) ?(1)?(2)
?(1)?(2) (-1)
?(1)?(2)
?(1)?(2)
(2) ?(1)?(2) S2
(2)½/2 ?(1)?(2) ?(1)?(2) (2)
(2)½/2 ?(1)?(2) ?(1)?(2)
?(1)?(2) (2)
?(1)?(2)
S 1 S(S1) 2 Ms 1, 0, -1
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Lets do one in detail Sz ?(1)?(2) Sz(1)
?(1)?(2) Sz(2) ?(1)?(2) ?(2) Sz(1) ?(1)
?(1) Sz(2) ?(2) ?(2) (1/2) ?(1) ?(1)
(1/2) ?(2) (½ ½) ?(1)?(2) (1) ?(1)?(2)
Sz(1) Sz(2) ?(1)?(2)