<s>
In	O
quantum	O
mechanics	O
,	O
the	B-General_Concept
Pauli	I-General_Concept
exclusion	I-General_Concept
principle	I-General_Concept
states	O
that	O
two	O
or	O
more	O
identical	O
particles	O
with	O
half-integer	O
spins	O
(	O
i.e.	O
</s>
<s>
In	O
the	O
case	O
of	O
electrons	O
in	O
atoms	O
,	O
it	O
can	O
be	O
stated	O
as	O
follows	O
:	O
it	O
is	O
impossible	O
for	O
two	O
electrons	O
of	O
a	O
poly-electron	O
atom	B-Language
to	O
have	O
the	O
same	O
values	O
of	O
the	O
four	O
quantum	O
numbers	O
:	O
n	O
,	O
the	O
principal	O
quantum	O
number	O
;	O
,	O
the	O
azimuthal	O
quantum	O
number	O
;	O
m	O
,	O
the	O
magnetic	O
quantum	O
number	O
;	O
and	O
ms	O
,	O
the	O
spin	O
quantum	O
number	O
.	O
</s>
<s>
Particles	O
with	O
an	O
integer	O
spin	O
,	O
or	O
bosons	O
,	O
are	O
not	O
subject	O
to	O
the	B-General_Concept
Pauli	I-General_Concept
exclusion	I-General_Concept
principle	I-General_Concept
:	O
any	O
number	O
of	O
identical	O
bosons	O
can	O
occupy	O
the	O
same	O
quantum	O
state	O
,	O
as	O
with	O
,	O
for	O
instance	O
,	O
photons	B-Application
produced	O
by	O
a	O
laser	O
or	O
atoms	O
in	O
a	O
Bose	O
–	O
Einstein	O
condensate	O
.	O
</s>
<s>
A	O
more	O
rigorous	O
statement	O
is	O
that	O
,	O
concerning	O
the	O
exchange	B-General_Concept
of	O
two	O
identical	O
particles	O
,	O
the	O
total	O
(	O
many-particle	O
)	O
wave	O
function	O
is	O
antisymmetric	O
for	O
fermions	O
,	O
and	O
symmetric	O
for	O
bosons	O
.	O
</s>
<s>
If	O
two	O
fermions	O
were	O
in	O
the	O
same	O
state	O
(	O
for	O
example	O
the	O
same	O
orbital	O
with	O
the	O
same	O
spin	O
in	O
the	O
same	O
atom	B-Language
)	O
,	O
interchanging	O
them	O
would	O
change	O
nothing	O
and	O
the	O
total	O
wave	O
function	O
would	O
be	O
unchanged	O
.	O
</s>
<s>
The	B-General_Concept
Pauli	I-General_Concept
exclusion	I-General_Concept
principle	I-General_Concept
describes	O
the	O
behavior	O
of	O
all	O
fermions	O
(	O
particles	O
with	O
"	O
half-integer	O
spin	O
"	O
)	O
,	O
while	O
bosons	O
(	O
particles	O
with	O
"	O
integer	O
spin	O
"	O
)	O
are	O
subject	O
to	O
other	O
principles	O
.	O
</s>
<s>
Fermions	O
include	O
elementary	O
particles	O
such	O
as	O
quarks	B-Operating_System
,	O
electrons	O
and	O
neutrinos	O
.	O
</s>
<s>
Additionally	O
,	O
baryons	O
such	O
as	O
protons	B-Application
and	O
neutrons	O
(	O
subatomic	O
particles	O
composed	O
from	O
three	O
quarks	B-Operating_System
)	O
and	O
some	O
atoms	O
(	O
such	O
as	O
helium-3	O
)	O
are	O
fermions	O
,	O
and	O
are	O
therefore	O
described	O
by	O
the	B-General_Concept
Pauli	I-General_Concept
exclusion	I-General_Concept
principle	I-General_Concept
as	O
well	O
.	O
</s>
<s>
The	B-General_Concept
Pauli	I-General_Concept
exclusion	I-General_Concept
principle	I-General_Concept
underpins	O
many	O
properties	O
of	O
everyday	O
matter	O
,	O
from	O
its	O
large-scale	O
stability	O
to	O
the	O
chemical	O
behavior	O
of	O
atoms	O
.	O
</s>
<s>
Bosons	O
include	O
the	O
photon	B-Application
,	O
the	O
Cooper	O
pairs	O
which	O
are	O
responsible	O
for	O
superconductivity	O
,	O
and	O
the	O
W	O
and	O
Z	O
bosons	O
.	O
</s>
<s>
In	O
the	O
1916	O
article	O
"	O
The	O
Atom	B-Language
and	O
the	O
Molecule	O
"	O
by	O
Gilbert	O
N	O
.	O
Lewis	O
,	O
for	O
example	O
,	O
the	O
third	O
of	O
his	O
six	O
postulates	O
of	O
chemical	O
behavior	O
states	O
that	O
the	O
atom	B-Language
tends	O
to	O
hold	O
an	O
even	O
number	O
of	O
electrons	O
in	O
any	O
given	O
shell	O
,	O
and	O
especially	O
to	O
hold	O
eight	O
electrons	O
,	O
which	O
he	O
assumed	O
to	O
be	O
typically	O
arranged	O
symmetrically	O
at	O
the	O
eight	O
corners	O
of	O
a	O
cube	O
.	O
</s>
<s>
In	O
1919	O
chemist	O
Irving	O
Langmuir	O
suggested	O
that	O
the	O
periodic	O
table	O
could	O
be	O
explained	O
if	O
the	O
electrons	O
in	O
an	O
atom	B-Language
were	O
connected	O
or	O
clustered	O
in	O
some	O
manner	O
.	O
</s>
<s>
In	O
1922	O
,	O
Niels	O
Bohr	O
updated	O
his	O
model	O
of	O
the	O
atom	B-Language
by	O
assuming	O
that	O
certain	O
numbers	O
of	O
electrons	O
(	O
for	O
example	O
2	O
,	O
8	O
and	O
18	O
)	O
corresponded	O
to	O
stable	O
"	O
closed	O
shells	O
"	O
.	O
</s>
<s>
The	B-General_Concept
Pauli	I-General_Concept
exclusion	I-General_Concept
principle	I-General_Concept
with	O
a	O
single-valued	O
many-particle	O
wavefunction	O
is	O
equivalent	O
to	O
requiring	O
the	O
wavefunction	O
to	O
be	O
antisymmetric	O
with	O
respect	O
to	O
exchange	B-General_Concept
.	O
</s>
<s>
Antisymmetry	O
under	O
exchange	B-General_Concept
means	O
that	O
.	O
</s>
<s>
This	O
implies	O
when	O
,	O
which	O
is	O
Pauli	B-General_Concept
exclusion	I-General_Concept
.	O
</s>
<s>
In	O
relativistic	O
quantum	O
field	O
theory	O
,	O
the	O
Pauli	B-General_Concept
principle	I-General_Concept
follows	O
from	O
applying	O
a	O
rotation	O
operator	O
in	O
imaginary	O
time	O
to	O
particles	O
of	O
half-integer	O
spin	O
.	O
</s>
<s>
The	O
reason	O
for	O
this	O
is	O
that	O
,	O
in	O
one	O
dimension	O
,	O
the	O
exchange	B-General_Concept
of	O
particles	O
requires	O
that	O
they	O
pass	O
through	O
each	O
other	O
;	O
for	O
infinitely	O
strong	O
repulsion	O
this	O
cannot	O
happen	O
.	O
</s>
<s>
In	O
momentum	O
space	O
,	O
the	O
exclusion	O
principle	O
is	O
valid	O
also	O
for	O
finite	O
repulsion	O
in	O
a	O
Bose	O
gas	O
with	O
delta-function	O
interactions	O
,	O
as	O
well	O
as	O
for	O
interacting	O
spins	O
and	O
Hubbard	B-Algorithm
model	I-Algorithm
in	O
one	O
dimension	O
,	O
and	O
for	O
other	O
models	O
solvable	O
by	O
Bethe	O
ansatz	O
.	O
</s>
<s>
The	B-General_Concept
Pauli	I-General_Concept
exclusion	I-General_Concept
principle	I-General_Concept
helps	O
explain	O
a	O
wide	O
variety	O
of	O
physical	O
phenomena	O
.	O
</s>
<s>
An	O
electrically	O
neutral	O
atom	B-Language
contains	O
bound	O
electrons	O
equal	O
in	O
number	O
to	O
the	O
protons	B-Application
in	O
the	O
nucleus	O
.	O
</s>
<s>
Electrons	O
,	O
being	O
fermions	O
,	O
cannot	O
occupy	O
the	O
same	O
quantum	O
state	O
as	O
other	O
electrons	O
,	O
so	O
electrons	O
have	O
to	O
"	O
stack	O
"	O
within	O
an	O
atom	B-Language
,	O
i.e.	O
</s>
<s>
An	O
example	O
is	O
the	O
neutral	O
helium	O
atom	B-Language
,	O
which	O
has	O
two	O
bound	O
electrons	O
,	O
both	O
of	O
which	O
can	O
occupy	O
the	O
lowest-energy	O
(	O
1s	O
)	O
states	O
by	O
acquiring	O
opposite	O
spin	O
;	O
as	O
spin	O
is	O
part	O
of	O
the	O
quantum	O
state	O
of	O
the	O
electron	O
,	O
the	O
two	O
electrons	O
are	O
in	O
different	O
quantum	O
states	O
and	O
do	O
not	O
violate	O
the	O
Pauli	B-General_Concept
principle	I-General_Concept
.	O
</s>
<s>
In	O
a	O
lithium	B-Language
atom	B-Language
,	O
with	O
three	O
bound	O
electrons	O
,	O
the	O
third	O
electron	O
cannot	O
reside	O
in	O
a	O
1s	O
state	O
and	O
must	O
occupy	O
one	O
of	O
the	O
higher-energy	O
2s	O
states	O
instead	O
.	O
</s>
<s>
To	O
test	O
the	B-General_Concept
Pauli	I-General_Concept
exclusion	I-General_Concept
principle	I-General_Concept
for	O
the	O
helium	O
atom	B-Language
,	O
Gordon	O
Drake	O
carried	O
out	O
very	O
precise	O
calculations	O
for	O
hypothetical	O
states	O
of	O
the	O
He	O
atom	B-Language
that	O
violate	O
it	O
,	O
which	O
are	O
called	O
paronic	O
states	O
.	O
</s>
<s>
Many	O
mechanical	O
,	O
electrical	O
,	O
magnetic	O
,	O
optical	O
and	O
chemical	O
properties	O
of	O
solids	O
are	O
the	O
direct	O
consequence	O
of	O
Pauli	B-General_Concept
exclusion	I-General_Concept
.	O
</s>
<s>
The	O
stability	O
of	O
each	O
electron	O
state	O
in	O
an	O
atom	B-Language
is	O
described	O
by	O
the	O
quantum	O
theory	O
of	O
the	O
atom	B-Language
,	O
which	O
shows	O
that	O
close	O
approach	O
of	O
an	O
electron	O
to	O
the	O
nucleus	O
necessarily	O
increases	O
the	O
electron	O
's	O
kinetic	O
energy	O
,	O
an	O
application	O
of	O
the	O
uncertainty	O
principle	O
of	O
Heisenberg	O
.	O
</s>
<s>
However	O
,	O
stability	O
of	O
large	O
systems	O
with	O
many	O
electrons	O
and	O
many	O
nucleons	O
is	O
a	O
different	O
question	O
,	O
and	O
requires	O
the	B-General_Concept
Pauli	I-General_Concept
exclusion	I-General_Concept
principle	I-General_Concept
.	O
</s>
<s>
It	O
has	O
been	O
shown	O
that	O
the	B-General_Concept
Pauli	I-General_Concept
exclusion	I-General_Concept
principle	I-General_Concept
is	O
responsible	O
for	O
the	O
fact	O
that	O
ordinary	O
bulk	O
matter	O
is	O
stable	O
and	O
occupies	O
volume	O
.	O
</s>
<s>
This	O
suggestion	O
was	O
first	O
made	O
in	O
1931	O
by	O
Paul	O
Ehrenfest	O
,	O
who	O
pointed	O
out	O
that	O
the	O
electrons	O
of	O
each	O
atom	B-Language
cannot	O
all	O
fall	O
into	O
the	O
lowest-energy	O
orbital	O
and	O
must	O
occupy	O
successively	O
larger	O
shells	O
.	O
</s>
<s>
The	O
first	O
rigorous	O
proof	O
was	O
provided	O
in	O
1967	O
by	O
Freeman	O
Dyson	O
and	O
Andrew	O
Lenard	O
(	O
de	O
)	O
,	O
who	O
considered	O
the	O
balance	O
of	O
attractive	O
(	O
electron	O
–	O
nuclear	O
)	O
and	O
repulsive	O
(	O
electron	O
–	O
electron	O
and	O
nuclear	O
–	O
nuclear	O
)	O
forces	O
and	O
showed	O
that	O
ordinary	O
matter	O
would	O
collapse	O
and	O
occupy	O
a	O
much	O
smaller	O
volume	O
without	O
the	O
Pauli	B-General_Concept
principle	I-General_Concept
.	O
</s>
<s>
The	O
consequence	O
of	O
the	O
Pauli	B-General_Concept
principle	I-General_Concept
here	O
is	O
that	O
electrons	O
of	O
the	O
same	O
spin	O
are	O
kept	O
apart	O
by	O
a	O
repulsive	O
exchange	B-General_Concept
interaction	I-General_Concept
,	O
which	O
is	O
a	O
short-range	O
effect	O
,	O
acting	O
simultaneously	O
with	O
the	O
long-range	O
electrostatic	O
or	O
Coulombic	O
force	O
.	O
</s>
<s>
In	O
1995	O
Elliott	O
Lieb	O
and	O
coworkers	O
showed	O
that	O
the	O
Pauli	B-General_Concept
principle	I-General_Concept
still	O
leads	O
to	O
stability	O
in	O
intense	O
magnetic	O
fields	O
such	O
as	O
in	O
neutron	O
stars	O
,	O
although	O
at	O
a	O
much	O
higher	O
density	O
than	O
in	O
ordinary	O
matter	O
.	O
</s>
<s>
It	O
is	O
a	O
consequence	O
of	O
general	O
relativity	O
that	O
,	O
in	O
sufficiently	O
intense	O
gravitational	O
fields	O
,	O
matter	O
collapses	O
to	O
form	O
a	O
black	B-Application
hole	I-Application
.	O
</s>
<s>
Astronomy	O
provides	O
a	O
spectacular	O
demonstration	O
of	O
the	O
effect	O
of	O
the	O
Pauli	B-General_Concept
principle	I-General_Concept
,	O
in	O
the	O
form	O
of	O
white	O
dwarf	O
and	O
neutron	O
stars	O
.	O
</s>
<s>
In	O
neutron	O
stars	O
,	O
subject	O
to	O
even	O
stronger	O
gravitational	O
forces	O
,	O
electrons	O
have	O
merged	O
with	O
protons	B-Application
to	O
form	O
neutrons	O
.	O
</s>
<s>
However	O
,	O
even	O
this	O
enormous	O
rigidity	O
can	O
be	O
overcome	O
by	O
the	O
gravitational	O
field	O
of	O
a	O
neutron	O
star	O
mass	O
exceeding	O
the	O
Tolman	O
–	O
Oppenheimer	O
–	O
Volkoff	O
limit	O
,	O
leading	O
to	O
the	O
formation	O
of	O
a	O
black	B-Application
hole	I-Application
.	O
</s>
