Phase Difference Homework | Solutions in PDF

v_pino
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Homework Statement


Please see pdf file. Thank you.


Homework Equations





The Attempt at a Solution


 

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The work you've done so far is correct. Now substitute r1 and r2 into your phase difference equation, then use the suggested simplification.
 
How do I get rid of 'a' since the aperture size is not give?
 
I tried letting 'a' = 'y' but I'm a factor of two larger.
 
v_pino said:
How do I get rid of 'a' since the aperture size is not give?

Oh, I hadn't realized that. The given equation for phase shift actually has to be wrong, since phase shift must depend on aperture size. Imagine making the aperture extremely small, for example. The phase shift should logically go to zero, but in that equation, it doesn't.
 
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...
View full post »
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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