Expectation value of an operator in matrix quantum mechanics

Dixanadu
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Homework Statement


Hey everyone.
Imma type this up in Word as usual:

http://imageshack.com/a/img577/3654/q9ey.jpg

Homework Equations



http://imageshack.com/a/img22/3185/pfre.jpg

The Attempt at a Solution


http://imageshack.com/a/img703/8571/xogb.jpg
 
Last edited by a moderator:
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There's a mistake in the last step. You've overlooked the imaginary units in the exponentials!
 
Ohhh yea it isn't cosh, it should be cos...but is the rest okay? I mean the matrix U and stuff?
 
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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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