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I see in Griffiths (and in class) how we determined <math>v_g = \frac{d\omega}{dk}</math>. But how do we get <math>v_p = \frac{\omega}{k}</math>?

This is simply the relationship between frequency <math>f</math>, wavelength <math>\lambda</math>, and velocity <math>v</math> for any wave (<math>v=f\lambda</math>), written in slightly different terms. Instead of <math>f</math> and <math>\lambda</math> we have the wavenumber <math>k=\frac{2\pi}{\lambda}</math> and the angular frequency <math>\omega=2\pi f</math>.

The figure 2.10(b) in Griffiths is not correct because <math>\phi(k)</math> should be negative for some k, am I right?

Yuichi You are right. I never noticed this before.

What did everyone think of the test?

I think it was very good except for problem 1. I feel it is unfair to expect us to be able to do those integrals on the fly. Other than that, the professor did a very good job making a closed-book test that did not rely on memorization. Although I didn't do well, I walked out of the test feeling that it was my fault for not studying enough, not because the test was poorly-written. I think anyone who thoroughly went over the major proofs covered and the problems we were assigned should have been able to do well on all the problems except 1.

I agree with nikif002 totally, the integrals for 1 was out of the blues. Besides that, it was a fair test.

it might have helped to use the expression for x and p with the a+/a- operator, then you would not have to do integrals! and even though i forgot this on test myself, we should all remember it for the next test.

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