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*From*: Paolo Cavallo <ton0621@IPERBOLE.BOLOGNA.IT>*Date*: Sun, 15 Feb 2004 21:13:02 +0100

----- Original Message -----

From: SSHS KPHOX

To: PHYS-L@lists.nau.edu

Sent: Sunday, February 15, 2004 7:13 PM

Subject: A fermion question from a Chemistry teacher

I am an intruder from the Chemistry page in bad need of your expertise. The

doubts are related to the fermionic states, the school's term is beginning

in a fortnight and I would like to be ready for my students questions:

a) Can bosons break Pauli's exclusion principle??? How do you explain this

please??

b) Can somebody briefly explain how is it that paired fermions may behave

as bosons?? Is it because of the spin number??? Does it mean that they can

go from not being able to break Pauli's principle to be able to do so??

Only particles or systems with half-integer spin (fermions) obey to Pauli principle.

Particles or systems with integer spin (bosons) do not obey to it.

Paired fermions (as in Cooper pairs) have integer total spin, and behave as bosons.

Exclusion principle is only an intermadiate step to quantum statistics for half-integer

spin particles, which is Fermi-Dirac statistics. Integer spin particles follows Bose-

Einstein statistics.

Because quantum particles are indistinguishable, the wave function of a system of

identical particles must behave in one of two ways when you exchange two particles:

a) the wave function remains unchanged (symmetrical wave function );

b) the wave function reverses sign (antisymmetrical wave function ).

It can be shown that:

I) wave function of half-integer spin particles system reverse sign when two

identical particles are exchanged, while wave function of integer spin particles

system remains unchanged when two identical particles are exchanged;

II) if a system of particles has a symmetrical wave function it follows Bose-Einstein

statistics, and, if a system of particles has an antisymmetrical wave function it

follows Fermi-Dirac statistics.

I hope this will help you. Forgive my poor English.

Paolo Cavallo - Italy

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