Solve Schrödinger Equation: Need Help

schnuffi
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Homework Statement



Hi, I've just started this new course about quantum mechanics and it begins, among others, with this question:

[PLAIN]http://img710.imageshack.us/img710/2962/unbenanntfwg.jpg

I'm really at a loss how to approach this one. Can anyone please help?
 
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Well, what do you know? How familiar are you with the Schrödinger equation, and the concepts of operators, eigenfunctions, and eigenvalues?
 
Thanks for trying to help :D
I know the definitions of those terms that you have mentioned; but, I am not familiar with their mathematical components enough to use them to tackle the problem freely.
 
You've got to make an effort here if you want us to help you, schnuffi.

Suppose this were a problem on an exam. How would you start? Go back to your references (textbook, notes, etc.) and look things up, if you have to.
 
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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