Re: Pauli's exclusion principle

On 1 Dec 2003, ganesh wrote:

>    A basic Q: Is pauli's exclusion principle an axiom or can it be
> derived starting from the properties of electromagnetic force + .....??
> If so how??

Dear Ganesh, Pauli's exclusion principle has no relation to the
electromagnetic force. It is a consequence of the Fermi-Dirac statistics
that is obeyed by fermions - particles with half-integer spin.

The creation operator "a+" of a fermion and the annihilation operator "a"
satisfy

        {a,a+} = a (a+) + (a+) a = 1

Their anticommutator is one. Also, {a,a}=0 and therefore also {a+,a+}=0.
It follows that the number of states - the operator (a+)a - can only be 0
or 1. You can also see it from the fact that

        (a+ a)^2 = a+ a a+ a = a+ ( 1 - a+ a ) a = a+ a

i.e. the operator (a+)a squares to itself, and therefore its eigenvalues
must be 0 or 1 - the only numbers that square to themselves.

Pauli's exclusion principle is therefore a consequence of the fact that
the wavefunction of fermions is antisymmetric - it changes sign if you
permute two fermions. Consequently, the wavefunction must vanish if the
two fermions are located in the same state. Only 0 or 1 fermion can be
there in one state, and this fact is essential for chemistry to work, for
example, because we need the electrons to fill the different shells.

Best wishes
Lubos
______________________________________________________________________________
E-mail: [EMAIL PROTECTED]   fax: +1-617/496-0110   Web: http://lumo.matfyz.cz/
        phone:          work: +1-617/496-8199  home: +1-617/868-4487
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
      Superstring/M-theory is the language in which God wrote the world.