Physical meaning of wavefunction parameters x and t

[accountkiller]

This isn't a homework question per se but it's a question that I had while reading through my textbook so I think it's appropriate here. I just started studying Quantum Mechanics and so am getting familiarized with the meaning of wave functions and their behavior. One question I can't seem to find the answer to no matter what keywords I use in Google is the following:

What do the parameters of ψ(x,t) mean? When I imagine a 2D wave on a graph, I see a wave periodically going up and down along the x-axis, so parameter x (position). But the y-axis is not time, it's the amplitude. So where does the parameter 't' fit into this graph?

It feels like it should be a simple thing I should know but I do not and cannot find a good resource, so if anyone could help me understand its meaning, I'd appreciate it. Thanks1

 

[accountkiller]

Oh and similarly, another thing I don't quite understand and that I can't find on the internet is:

Where does the (kx-ωt) term come from in the wave function equation ψ(x,t) = ∫ A(k) e^i(kx-ωt) dk ? Essentially, I'm looking for a derivation of the wave function (typing that into Google somehow does not give me the right results).

 

[jtbell]

So where does the parameter 't' fit into this graph?

Imagine the graph is animated so the wave moves from left to right (or from right to left). Then to see what the graph looks like at a particular time, substitute the appropriate value of t. Different values of t give you "snapshots" of the wave (ψ versus x) at different times.

 

[Sonderval]

This page from my blog (in German) has some animations of complex wave functions
http://scienceblogs.de/hier-wohnen-...rodingergleichung-teil-iv-alles-im-kasten.php
that might be helpful.

 

[accountkiller]

jtbell: Ahh, thank you for that clear image! That's what I was looking for.

Sonderval: That is a pretty great blog you have there - I love that it's full of animations. I haven't gotten a chance to sit down and read it but I did skim over it and have added it to my Bookmarks to review when I get a free moment. Cool work!

Thank you both for the help :)

 

[Point Conception]

see : www.animations.physics.unsw.edu.au/jw/travelling_sine_wave.htm