What is the derivation of the Pauli Exclusion Principle?

[rayveldkamp]

I just finished a unit in statistical mechanics, and i have done some second year quantum mechanics and particle physics at university, however we have only been given the Pauli Exclusion principle and told that fermions obey it, but that bosons do not. My question is, does the Exclusion Principle have any deep derivation i.e: does it come out of the Schrödinger or Klein-Gordon equations, or is it simply a statement that works.

Ray

 

[scilover89]

I hope this will help you. I get this reply from a scientist when I asked him about Exclusion Principle.

"In quantum mechanics, the wave function psi(particle1, particle2) of
two fermions, such as electrons, must have the following property:

psi(particle1,particle2) = -psi(particle2,particle1)

So when the two particles are interchanged, the wave function changes
sign. If they are in the same quantum state, the wave function can't
change - so it must be zero. That is, there's zero probability that
the two particles can be in the same state. "

 

[Haelfix]

Actually it does have very deep roots. Its full derivation is a consequence of the mix of quantum mechanics and special relativity, quantum field theory. Without either one of those elements, you cannot logically have the so called spin-statistics theorem.

In my opinion, this is the single most compelling experimental reason to believe in all the weirdness of special relativity and quantum mechanics.

 

[dextercioby]

Actually it does have very deep roots. Its full derivation is a consequence of the mix of quantum mechanics and special relativity, quantum field theory. Without either one of those elements, you cannot logically have the so called spin-statistics theorem.

In its first (usually chemical useful) formulation,Pauli postulated the fact that 2 electrons could not be in the same quantum state.In the Dirac version of QM (the traditional formulation) is still kept as a postulate.Von Neumann used it to invent quantum statistical mechanics.And it was again Pauli who used indirectly (see below) to prove his theorem:the spin-statistics theorem (1940) is proven in the context of QED and a generalization to particle physics has been given by Lueders.
So my guess is it is the other way around.First postulate the symmetrization/antisymmetrization principle,then use it together with special relativity and quantization method to find out that there is a connection between spin ans statistics.
Allow me to quote from W.Pauli's famous article:"The Connection between spin and statistics."Phys.Rev.,58,p.716-722(1940) found in:"Wolfgang Pauli:<<Collected Scientific Papers>>",edited by R.Kronig and V.F.Weisskopf (1964,Interscience Pulblishers),Volume 2;p911-918:
Abstract:
"In the following paper we conclude for the relativistically invariant wave equation for free particles:From Postulate (I),according to which the energy must be positive,the necessity of Fermi-Dirac statistics for particles with arbitrary half-integer spin;from postulate (II),according to which observables on different space-time points with a space-like distance are commutable,the necessity of Einstein-Bose statistics for particles with arbitrary integer spin [...]"

In my opinion, this is the single most compelling experimental reason to believe in all the weirdness of special relativity and quantum mechanics.

In the same article,Pauli says:
"In conclusion we wish to state,that according to our opinion the connection between spin and statisics is one of the most important apllications of the special relativity theory".

 

[rayveldkamp]

Could you tell me where i can find a copy of that paper:
"The Connection between spin and statistics"
Thanks

 

[ZapperZ]

Could you tell me where i can find a copy of that paper:
"The Connection between spin and statistics"
Thanks

Note that dextercioby gave you the citation reference to the paper. However, if you meant where you could find it online without requiring a subscription access to Physical Review, then that's a different question.

I have given this link before (which, I think, made humanino weak in the knees after he discovered it), so here it is again. I probably should put it up in my Journal so that it can be easily found again for people who will be asking for something similar in about a month.

http://fangio.magnet.fsu.edu/~vlad/pr100/100yrs/html/chap14_toc.htm

This link should contain almost all of the landmark QM papers. So BOOKMARK it! :)

Zz.

 

[rayveldkamp]

Oh that is awesome, i can see my three moths uni holidays going by pretty fast now.
Thanks for that.

Ray