Why are the E-L-Equations the Same Old Song in the Music Industry?

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Homework Statement
Having trouble seeing how this derivative is being performed.
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EL equation
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The LyricsI'm afraid this one is a bit short, but I'm too lazy to extend it any more.I'm getting tired of the same old songThey play on the radioAnd I'm so sick of all the crapThat's on MTVThe lyrics are all so dumbAnd the melody's all wrongMy ears just can't take it no moreThat's why I sing this song(Chorus)It's the same old musicAll the timeI'm getting so boredOf the same old linesIt's the same old musicEverydayIt's driving me crazySo I gotta get awayThe beats and riffs they're all the sameNo originalityThe singers they sound all the sameIt's like it was meant to beIt's all too clear to meThat this music's gonna beStuck in my head all day longThat's why I sing this song(Chorus)BridgeI can't take it no moreIt's time to just ignoreThis terrible music they make(Chorus)
 
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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