Recent content by homer

This was a cool problem. Man I love Purcell.

By the symmetry of the problem sign of x,z doesn't matter, so I'll just take both positive. Then \lvert dz - a^2\vert = a^2 - dz and \lvert dz + a^2\rvert = dz + a^2, so the expression for the potential becomes \begin{align*} \varphi(x,0,z) & = \lambda\,\text{ln}\Big[...

I think I figured it out now. Always seems to happen right after I type up the whole problem here!

Let's just for the minute assume x > 0 also.

Homework Statement Purcell 2.10 [/B][not the problem I'm asking about, but needed for Purcell 2.11 which I am asking about] A thin rod extends along the z axis from z = -d to z = d. The rod carries a charge uniformly distributed along its length with linear charge density \lambda. By...

The integral was \langle \hat{p}\rangle = \int_{-\infty}^{\infty} dk\,\Big( \frac{2}{\pi a} \frac{\sin^2(ka/2)} {k^2} \Big)\,\hbar k = \frac{2\hbar}{\pi a} \int_{-\infty}^{\infty} dk\,\Big( \frac{\sin^2(ka/2)} {k} \Big) which was argued to...

Sounds like something worth checking out. Thanks for the recommendation.

Thanks bhobba! Maybe I'll take that course on distributions offered by coursera in January (though it's in French). Is distribution theory something I should study by itself, or is it something one would pick up studying grad level QM books?

E.g., if I have a time independent wavefunction \psi(x) with Fourier transform \tilde{\psi}(k), in computing the expectation of momentum are we calculating the principal value \lim_{R \to \infty} \int_{-R}^{R} dk\,\lvert \tilde{\psi}(k)\lvert^2\, \hbar k instead of the improper integral...

Oops, contour (1) should be from z = -\sqrt{a}R_1 - ib/2\sqrt{a} to z = -\sqrt{a}R_1.

Thanks Zeta. Huge brain fart on my part in making it rigorous. The integral I was trying to compute is the limit of I(R_1, R_2) = \int_{-R_1}^{R_2} e^{-ax^2 + bx}\,dx as R_1, R_2 \to \infty. Then I can make a subsitution z = \sqrt{a}(x-ib/2a) to get the integral I(R_1,R_2) =...

Homework Statement Let a,b be real with a > 0. Compute the integral I = \int_{-\infty}^{\infty} e^{-ax^2 + ibx}\,dx. Homework Equations Equation (1): \int_{-\infty}^{\infty} e^{-x^2}\,dx = \sqrt{\pi} Equation (2): -ax^2 + ibx = -a\Big(x - \frac{ib}{2a}\Big)^2 - \frac{b^2}{4a}The Attempt...

Don't proofs always look so beautiful in the book or when your professor is writing them at the board? Well those proofs in the book are all later drafts and the proof your prof writes so cleanly is the same one he's been writing on the board every semester or two for years. A few years ago I...

I started it out with a few of us who take math and physics MOOCs on coursera and edx, but everyone's too busy and it looks like no one else wants to do the course. I'm just doing it on my own and I think I'll come here when I have questions. I have been writing PDF notes (for some reason...

MIT OCW recently posted their introductory quantum class 8.04 at http://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/ I was wondering if anyone would be interested in going through the course. I'm primarily studying it to get ready for the MIT MOOC 8.05x Quantum Physics...