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Re: A fermion question from a Chemistry teacher

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