Solving Tensor Problem: Need Help Now!

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Spent several hours in the library on this and i have no idea how to do...

please help I'm going to burst out with tears soon...
 

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I can't make sense of any of that. Does Aijkl=Fijkl(am) mean that Aijkl is the result of letting Fijkl act on am? Then why doesn't A have five indices instead of four? Is am a vector or a component of a vector? Why doesn't m appear anywhere on the right? What are the definitions of A·B and A-1? (I haven't seen either defined for tensors with 4 indices). Does A denote the tensor and Aijkl its components in a coordinate system? Then what does A (no indices, not bold) denote?
 
Looks to me like F just takes a six-tuple of coefficients (what kind, who knows?) and spits out a rank-4 tensor. In other words, F is some six-parameter family of tensors. I suppose the answers will be in terms of the a_i's and b_i's (i=1,...,6).
 
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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