Re: Looking for examples of Physically-Meaningful, Non-Gaussian Wavefunctions

On Wed, 30 Apr 2008 01:36:32 -0400, "Jay R. Yablon"
<jyablon@xxxxxxxxxxxx> wrote:

It is well known that a Gaussian wavefunction, such as:

psi (x) = exp [Ax^2 + Bx} (1)

has an uncertainty that satisfies the equality, not the inequality, in
the Heisenberg relationship, that is:

delta x delta p = 1/2 hbar (2)

for a Gaussian wavefunction.


[Hammond]
Yes of course, this is a result of classical statistics
not quantum theory, since in classical statistics the so
called "Heisenberg Uncertainty Principle" is simply a
consequenc of the fact that the Fourier transform of a
Gaussion distribution is another Gausian, hence the equality
is due to the minimum variance property of the two
(Gaussian) Standard Deviations involved.

I was hoping that someone can point me toward some physically-meaningful
wavefunctions psi(x) which are NOT Gaussians, i.e., wavefunction which,
after we Fourier transform them into psi(p) and then take the variance,
end up satisfying the inequality:

delta x delta p > 1/2 hbar (2)

I am looking, again, for wavefunctions that are physically meaningful,
which I suppose would mean that they are solutions to a field equation
or in some other way underlie observable physics.

[Hammond]
I would expect that asymmetric distributions
(non-Gaussian) might result from strong non-uniform applied
fields, something like the Paschen-Back effect since it is
known to be a "non-linear effect".

Especially, I am interested in what one might take to be a non-Gaussian
wavefunction for a charged lepton, e.g., electron.

Thanks,

Jay.
____________________________
Jay R. Yablon
Email: jyablon@xxxxxxxxxxxx
co-moderator: sci.physics.foundations
Weblog: http://jayryablon.wordpress.com/
Web Site: http://home.nycap.rr.com/jry/FermionMass.htm
.

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