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Pauli
exclusion principle
The overall wavefunction
Ψ
(space AND
spin) must change sign when swap the
quantum numbers of any 2 electrons
Consequence:
no two electrons can have
the same set of quantum numbers .
Ψ
ab
=

Ψ
ba
1st slot: electron 1
quantum numbers
(space and spin)
2nd slot: electron 2
quantum numbers
For
two
electrons, the possible wavefunctions are:
Ψ
=
ψ
sym
χ
anti
Ψ
=
ψ
sym
χ
anti
OR
ψ
sym
= [
ψ
n
(
x
1
)
ψ
m
(
x
2
)
+
ψ
m
(
x
1
)
ψ
n
(
x
2
)]/2
1/2
ψ
anti
= [
ψ
n
(
x
1
)
ψ
m
(
x
2
)

ψ
m
(
x
1
)
ψ
n
(
x
2
)]/2
1/2
"
anti
=
[
#
1
$
2
%$
1
#
2
]/2
1/ 2
sym
=
[
#
1
$
2
+
$
1
#
2
]/2
1/ 2
"
1
"
2
"
1
"
2
“singlet”: total S= 0 (
both
spins;
each has individual spin quantum
number S=1/2)
3 “triplet” states,
each with total S=1
Quantum
numbers of
electrons 1 and
2 are swapped
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 Spring '08
 Freedman
 Physics

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