The Poisson Integral Formula is a representation of the bounded solution of the Dirichlet problem for Laplace's equation in the interior of the disc. Derive the corresponding formula
for the Dirichlet problem in the exterior of the disc, again assuming that the solution is bounded.So we derived...
I believe that the standard book for mathematical methods of physics is still "Mathematical Methods in the Physical Sciences" by Boas.
For pure math, check out http://hbpms.blogspot.com/" . Someone posted it a while back, and it seems to be a really comprehensive list of books.
The thing that immediately jumps out at me would be studying how horses run and jump. You could analyze the forces involved and try to figure out different ways to optimize the process (weight, leg length, angle of jump, etc.). I'm sure this has been studied from a biological perspective, but...
Not knowing the scores you got on each individual section makes it hard to say anything, since you could've done great on one part and terrible on another.
According to the ETS website:
There might be a minor statistical advantage one way or the other, but it's impossible to say whether or not it would've been better for your particular case. I'm a cautious person, so I would say it's better to take the +0 than risk losing points, but that's...
Homework Statement
A total charge q is distributed uniformly along a ring of radius b. The ring is in the x-y plane centered on the origin. The multipole expansion is not valid for r<b. Find an expansion for the potential valid in this regionHomework Equations
The charge density is just...
Oh, so do I just find the coefficients corresponding to the 3/2 case and do a linear combination of them (using the appropriate coefficients from the table) and then do the same thing for the 1/2 case?
Yeah, all of that means nothing to me. I double checked in the index and neither "tensor...
While that does seem like an easier way to do it, the point of the exercise is to learn how to read off the values from a table (see attached picture). Clearly I'm looking for something in the 1x1/2 table (second picture), but beyond that I'm lost.
Right, but I am having trouble seeing how it's possible to move forward without knowing M, m_1 or m_2.
From what I can tell, the furthest I can go is to say
\sum_{m_1+m_2=M}C^{1,\frac{1}{2},J}_{m_1,m_2,M}\mid 1 m_1\rangle \mid \frac{1}{2} m_2\rangle
Homework Statement
Find the Clebsch-Gordan coefficients associated with the addition of two angular momenta j_1 = 1 and j_2 = \frac{1}{2}
Homework Equations
The table of coefficients.
The Attempt at a Solution
I think I am misunderstanding something important here. I can't see...
Our book only mentions the special cases of the virial theorem for stationary states ,2<T>=<x\frac{dV}{dx}>, and stationary states of the harmonic oscillator, <T>=<V>.
Even if I use your version of it, though, I don't see how that helps.
Homework Statement
Given the potential energy V(r)=-\frac{1}{4\pi \epsilon_0}\frac{e^2}{r} (where e is the unit charge), use the uncertainty principle \Delta x \Delta p \geq \hbar to find the Bohr radius r_B for a hydrogen atom and the ground state energy E_0.
Hint: write down the kinetic...
While I agree with the spirit of the arguments made in favor of taking humanities courses (which, for the record, I agree with completely), the reality can be a lot more annoying .
For me, at least, the only thing I've gotten out of my humanities courses have been recurring nightmares about...