Nevermind, I solved my questions after a discussion with a friend.
1) Units issue comes from the normalization
2) Imaginary issue comes from the fact that I forgot to take the conjugate of R
If anyone comes across this and wants a more detailed explanation, feel free to pm me
I don't think you have to make any assumptions, just examine closely for the necessary functional form and whether it's possible given the domain of the integral...
What did you have in mind? Maybe write out your line of thinking so I can get a better idea of where you are getting stuck...
Regarding Q2: Yup! It's almost the definition of the function I'm thinking of itself: have you seen it before?
Except there's a crutial part to the limits of your integral that you would have to pay close attention to in order to understand whether the function is actually a viable...
Start out by writing out the definition of the laplace transform explicitly in terms of the unknown function ##f(t)##. Knowing that you want the integral to evaluate to ##e^s##, you should be able to see what kind of function would be necessary to satisfy the equation. (*Hint: it's the kind of...
Another formula (related to the one you mentioned, but derived from the wavelength) gives the wave velocity directly in terms of the freqency and string length. Try this one?
$$ f = \frac{v}{2 L} $$
For tensor actions in general, I always started by thinking about the properties in lower dimensional spaces, where they can make more physical sense or can be mapped out/drawn explicitly on paper. It tends to bolster your intuition for what happens with higher rank objects.
Then, you can just...
Right, so I pretty much gave you an explicit roadmap to get that exact answer.
You are going to have to do some more work and at least try to work it out using what I've already told you. (You are 75% there already).
If you have more questions, post how far you get and I'll be happy to answer...
You happened to pick an element that has an exception to the rules->bad break! The wiki article http://en.wikipedia.org/wiki/Electron_configuration has a fairly good explanation as to what order to write the shells and how many electrons can fit in each.
Finally, in case you were confused...
I think you might have a typo here, because that doesn't equal 0. Nevertheless, if you work out the partials and do get 0 (I checked it out quickly and seem to also get 0), then the closed contour integral should also go to zero. What makes you suggest that it is wrong?
Also, note in your...
Don't know if this post is still important to you since it's a little old, but your expression for the divergence in polar coordinates is incorrect, as there are extra factors in the formula (it's not the same as you would in Cartesian). Take another look at it.
See here...
In general, I try to avoid telling people whether their numerical answers are correct. This is mainly because if I make the same calculator mistake you do, and tell you the answer is right, I'll feel super guilty when it comes back with red ink and you yell at me for misleading you ^^;
If you...
Your general solution is just the sum of each independent solution by superposition with constants to be found from initial conditions. Build each independent solution from the eigenvector multiplied by the exponential of the eigenvalue multiplied with the dependent variable.
For example...