Gaussian Functions In Quantum Mechanics

I guess the question is, is this ever used as an operator on Psi?  The only thing I've seen Gaussians used for (although I'm sure they get used for all kinds of stuff) is various types of computerized visual recognition software.  

i.e. http://en.wikipedia.org/wiki/Blob_detection 

That's kind of what I thought. Lots of people throwing around Frederick's name here but what does it all mean. Heard a great saying yesterday you would appreciate Patzer, It has to be simple in order to work. A lot like the razor's cutting edge. OK, how do we apply the Gaussian function to psi? And what would it mean?

That's what I still am trying to find out. That's why I've been looking around, Gaussian functions have a lot to do with everything, and anything with physics with them deserves immediate attention here.

I've heard about Gaussian stuff a lot, like Gaussian wave packets. Anybody got a clue what a Gaussian wave packet is? Uh, do we apply some Gaussian transform to a wave function? It seems that what we need here is a Gaussian function applied in a quantum mechanical calculation with the math shown so we can follow it. I think that is your quest Strangequark. Futhermore, what is your favorite colour?

Well, ok this is going to be long-winded. So we have the quantum version of the classical harmonic oscilator. What is interesting to note here is that we get only one unique value from this, that is, it is deterministic. Next, we have the ground state of this. This stationary state is an eigenstate of a Hamiltonian Function. Now, a Hamiltonian Function in this case is the whole wavefunction of all this stuff. I need to do more research about this "wave packet" stuff when I have more time.

My favorite color is blue becuase I am thoughtful and loyal (or at least try to be!). My second favorite color is green becuase it also is a calming, rich, and easy color. So far as I know green is associated with intelligence and jealousy. I am not asking you to buy into the psychological interpretations, but what are your two favorite colors?

You should not have two favorite colours or you will not be able to cross the bridge to the Castle Arrrggghhhhh. 

Let me read over what you've written. Quantum version of the classical harmonic oscillator?

Generally in GRW when a hit occurs at h, the waveform is multiplied by e^(-(d^2)/2 * (r-h)^2) (which is Gaussian) and then normalized. d represents how closely the particle is localized, r the location of the particle, and h the location of the 'hit'.

On the topic of operators vs. functions, an operator is a function. When we use it in this matter, multiplying it by the waveform function to produce a new function, it is termed an operator.

Thanks for the handy equation and the clarification, rubixcuber.