TICC Forum for CSM

[klarson]

 Schrodinger dispersion

[ckelso]

Remember that one way to represent a dispersion relation is a relationship between omega and k for a wave. If omega = speed * k, and speed is a constant, then there is no dispersion and the group velocity is the same as the wave/phase velocity.

If you work out problem 9.22 (b), you are essentially finding the Schrodinger dispersion relation. The idea is that the group velocity is something different from the wave velocity.

So to construct the Mathematica, I recommend that you work in units of hbar and m, i.e. set hbar=1 and m=1. You can use the ideas presented in 9.22 (b) to get omega as a function of k. So when you look at two (or more) waves with slightly different momenta, this will set the wave velocity (omega/k) to be different for the waves. So when you combine them and plot them, you will see the difference between the phase velocity and the group velocity. The way I animated the thing is I generated a graph as a function of x at a specific time. I then incremented the time up a little amount delta t, and then made the graph again. I did this many times (using a do loop) and got a whole bunch of graphs. If you then double click on one of the graphs, it will animate. If you want the thing to give a continuous loop then you need to make sure that the total time shown is an integer times the period, but that is by no means essential.

I hope this helps. If you need more, just let me know.

Kelso

[dones]

 

[arco]

I was actually fascinated after
accepting this topic .
After all, if you wish
to gain knowledge about PH462 Summer 2007and
get a good
essay about it, click this great essay service and simply
enjoy your free time.[/url]

[dantin]

Thank you a lot for the news just about essay! I heard that the writing service can make the essay writing. Moreover, that’s a very good chance to buy term papers orcustom essays referring to essay.

[AndrewLukas]

 Look it`ll help you!!!!!