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Science Forum Index » Physics - Research Forum » Looking for examples of Physically-Meaningful, Non-Gaussian Wavefunctions
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| Jay R. Yablon |
 Posted: Thu May 01, 2008 4:39 pm |
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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@nycap.rr.com
co-moderator: sci.physics.foundations
Weblog: http://jayryablon.wordpress.com/
Web Site: http://home.nycap.rr.com/jry/FermionMass.htm |
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| vivishek |
| Posted: Sat May 03, 2008 11:20 am |
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Quote: 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.
Examples of wavefunctions which are non-gaussian and still have a
physical relevance abound in quantum optics. These states are
solutions of the quantised maxwell equations for the electromagnetic
field. But of course, these wavefunctions have no representation in
the position basis and are only meaningful in the number basis of the
field. States like the binomial state, negative binomial state,
squeezed state are examples of purely non-gaussian states. On the
other hand, there are states like the glauber-lachs state which is a
superposition of a thermal state over an underlying gaussian state
(physically realised as the addition of a few thermal photons into a
cavity filled with laser light). |
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| John Park |
| Posted: Sat May 03, 2008 11:20 am |
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Guest
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"Jay R. Yablon" (jyablon@nycap.rr.com) writes:
Quote: 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.
Any solution of the Schroedinger equation for the hydrogen atom (or by
extension other atoms). The solutions of the simple harmonic oscillator are
not strictly gaussians (gaussian x polynomial). Aren't there plane wave wfs
and such for electrons in solid-state physics?
--John Park |
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