Recent content by nathan12343

There are certain approximations - things you neglected - that a more careful treatment will not neglect. Consider: the electron is actually a relativistic particle, yet you used the nonrelatavistic Schrödinger equation to derive those energy levels. Look up the fine structure of the...

Part iv is actually pretty easy. Find the total CM energy-momentum 4-vector, and calculate the invariant mass (<E,E> = \frac{1}{c^2}\sqrt{E^2 - (pc)^2}). You can also do part iii using this information as well as some Lorentz transformations... might save you a bit of tedious algebra, although...

Sounds right to me :)

Well, you know what the pattern from TWO slits looks like, so you're most of the way there. Three slits is the same thing as three pairs of slits, three double-slit patterns superposed on each other. The rest is just some moderately complicated algebra.

Kittel wants everything in units of the maximum energy of the lowest energy band, which happens to be 3/4 modulo a bunch of constants.

It problably doesn't matter since this thread is several months old, but anyway, the plot posted above is incorrect, all values should be multiplied by 4/3. Franz101010 did not normalize the energies correctly. See the attached mathematica notebook.

Really? It seems like a simple problem...

Can anyone help?

Because the unit vectors are actually functions of position in cylindrical coordinates. This means all the derivative in the gradient operator act not only on the components of a particular vector, but also the unit vectors themselves.

Homework Statement Solve Laplace's equation inside a circular annulus (a<r<b) subject to the boundary conditions \frac{\partial{u}}{\partial{r}}(a,\theta) = f(\theta)\text{, }\frac{\partial{u}}{\partial{r}}(b,\theta) = g(\theta) Homework Equations Assume solutions of the form u(r,\theta)...

Please disregard this - I meant to post in Calculus & Beyond.

Homework Statement Solve Laplace's equation inside a circular annulus (a<r<b) subject to the boundary conditions \frac{\partial{u}}{\partial{r}}(a,\theta) = f(\theta)\text{, }\frac{\partial{u}}{\partial{r}}(b,\theta) = g(\theta) Homework Equations Assume solutions of the form u(r,\theta)...

What you've written isn't exactly right, it isn't I=\int_{V}\frac{1}{\left|\texbf{x}\right|}d^{3}\texbf{x} It's, I=\int_{V}\frac{1}{\texbf{r}}d^{3}\texbf{x} with r = \sqrt{x^2 + y^2 + z^2} . Try doing that integral, it'll converge.

Homework Statement Solve Laplace's equation inside the rectangle 0 \le x \le L, 0 \le y \le H with the following boundary conditions u(0,y) = g(y)\text{, } u(L,y) = 0\text{, } u_y(x,0) = 0\text{, and } u(x,H) = 0 Homework Equations The Attempt at a Solution I know that with...

Wow, that was a really hard problem... Thanks, for the help, tiny-tim! If you wouldn't mind my asking, how did you come up with that?