Graph of a wave function and how to work out velocity from it.

Rich667
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Homework Statement


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Homework Equations





The Attempt at a Solution



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I really struggled with this one, my answer is nothing more than an incomplete educated guess.
 

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In terms of the wave-function... graphically (or visually) speaking... what does "velocity" mean?
 
"Velocity" means the speed the object (or in this case wave) is moving at in a certain direction.

But I don't know how to obtain the value of Velocity from the graph (that I still do not know how to draw).
 
At some time t=T, consider a snapshot of the graph. Focus on particular point (a bump, if wish) located at x=X on the graph. So, that feature has height H=g( 0.5X - 3T ). As T increases, what happens to that feature [keeping that height the same (which means keeping constant (0.5X - 3T) ]?

It might help to redraw your function at various times t (as suggested in your assignment).
 
Thread 'Need help understanding this figure on energy levels'

Thread 'Need help understanding this figure on energy levels'

This figure is from "Introduction to Quantum Mechanics" by Griffiths (3rd edition). It is available to download. It is from page 142. I am hoping the usual people on this site will give me a hand understanding what is going on in the figure. After the equation (4.50) it says "It is customary to introduce the principal quantum number, ##n##, which simply orders the allowed energies, starting with 1 for the ground state. (see the figure)" I still don't understand the figure :( Here is...
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Thread 'Understanding how to "tack on" the time wiggle factor'

Thread 'Understanding how to "tack on" the time wiggle factor'

The last problem I posted on QM made it into advanced homework help, that is why I am putting it here. I am sorry for any hassle imposed on the moderators by myself. Part (a) is quite easy. We get $$\sigma_1 = 2\lambda, \mathbf{v}_1 = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \sigma_2 = \lambda, \mathbf{v}_2 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \\ 0 \end{pmatrix} \sigma_3 = -\lambda, \mathbf{v}_3 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \end{pmatrix} $$ There are two ways...
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