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

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.

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.

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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