Re: Whence Degeneracy Pressure?

["John S. Denker" <jsd@MONMOUTH.COM>]

Regarding Mike Monce's comment:
> > fermions aren't forbidden from
> > being in the same state; the total wavefunction goes to zero in that case.
> > the superposition yields a 'node'.

David Bowman wrote:
> Those are two related but different effects.

I agree.  Emphasis on "different".

To make it completely explicit:  Consider the wave
        phi = 0.13 sin(2pi x)
which has a node whenever x is a half-integer.
It has a magnitude of 0.13 at the anti-nodes.

Contrast that with:
        z = 0.0 sin(2pi x)
which has no nodes, no anti-nodes, no wavelength,
no phase, and zero amplitude.  It's no wave at all.
It's the unwave.

Multiple fermions are _strictly_ forbidden from
being in the same state (considering spin and
spatial wavefunction together, as we should).
If you try it you don't get a node;  you get
no wave at all.

In a many-body problem there is such a thing as
the vacuum state, representing the state where
there are zero particles.  Call it |vac>.  It's
a perfectly good state.
Now, if you apply the same creation operator twice
(starting from that state or any other state)
the result is not |vac>, the result is nothing
at all.  The unstate.  Zilch.  Not |vac> but
0.0 |vac>, which is not at all the same.