Getting Started with Gaussian Wavepackets & Uncertainty Principle

[thegaussian]

I'm starting a project on Gaussian Wavepackets, and the evolution of the Uncertainty principle with time, however after the summer I'm a bit rusty :s, so I have a few questions, if anyone could help that would be great.

Ok, first of all I see (and largely understand) that delta-x delta-p > h-bar/2, but I would like to know how delta-x = RMS(x)? It's probably basic but I need good foundations...

Also, what is the general equation for a gaussian wavepacket?

Any help would be great, thanks!

 

[michael879]

delta-x = RMS(x) is the definition of delta-x. What else is there to understand? there's no physical meaning to the relation, its just what delta-x is defined as.

as for the general equation of the gaussian wavepacket, I believe it is just the free particle wave function multiplied by a gaussian function.

 

[jtbell]

Try a Google search for Gaussian wave packet.

 

[michael879]

Try a Google search for Gaussian wave packet.

Yea I was going to say that, except I actually tried doing that search and I just could not find a general equation for the gaussian wave packet.

 

[jtbell]

The http://musr.physics.ubc.ca/~jess/p200/gwp/gwp.html that I see has a rather detailed discussion of Gaussian wave packets, including the derivation of an explicit form of the initial wave function for one.

A full, explicit, time-dependent wave function that contains the spreading is another matter. I know it's in at least one textbook, Morrison's "Understanding Quantum Physics." The link above doesn't have that, but it does have an equation for the width of the packet as a function of time.