I solved my own problem. For anyone who's interested, I missed a factor of x in my integration, so that the dot product should actually be
<\psi_n|\frac{d\psi_n}{dR}>=\frac{1}{R}\int\frac{2n\pi x}{R^2}Cos[\frac{n \pi x}{R}]Sin[\frac{n \pi x}{R}]-Sin^{2}[\frac{n \pi x}{R}]dR=0
Therefore, gamma...
Homework Statement
I'm trying to find the geometric phase for the adiabatic widening of the infinite square well. Griffiths defines the geometric phase to be:
\gamma=i* \int^{w2}_{w1}<\psi_{n}|\frac{d\psi_{n}}{dR}>dR
Where R is the aspect of the potential that is changing and w1, w2 are the...
To strengthen your mathematical foundation, you really just have to do problems. But none of us really know where your weak points are... That's something that only you know. At my college, Linear Algebra is mostly facts and simple calculation. There's not much in that course that I think...
I'm a Sophomore at a Pennsylvania state university and my GPA is around a 3.4. I was hoping to get some kind of research opportunity over the summer. I've been looking for REU's using the NSF's list on their website and a website called compadre.com. However, these are pretty competitive, and...
Biconditional statements with "Or"
If I have a biconditional statement like this: Let p be an integer other than 0, -1, +1. Prove that p is prime if and only if for each a that exists in Z either (a, p) =1 or p|a.
I know that when you have a biconditional, you have to prove the statement...
I know that they all share no prime factors. If they did, they would have a GCD other than one. However, I don't know how to incorporate that (Or much at all) into a proof. I'm having a bit of trouble because I skipped into this course without taking the pre-req where you learn a lot of proof...
I'm not sure if it goes here or the section beyond calculus, so I'm just putting it here because it doesn't involve any calculus.
Homework Statement
Suppose that (a,b)=1 [Greatest Common Divisor=1] and (a,c)=1. Does (bc, a)=1?
Homework Equations
(a,b)=d=au+bv, where u and v are...
I go to a small state university in Pennsylvania. I'll probably end up with a dual major in Physics and Math, possibly a minor in Comp Sci. But here's my issue: My university is really not meant for Physics. It has a really small department, and there aren't that many high-level courses...
Carroll's book Spacetime and Geometry is actually what I'm using. It's tough though, because I don't have a very good mathematical background. I've never worked with tensors before this, so I quickly get lost, as Carroll mostly takes tensor manipulation for granted.
So to find a transformation that preserves the metric tensor in a space that is not Minkowski, I use the Killing equations to find Killing vectors?
I'll definitely take a look at Killing vectors in a gtr book. Thanks!
What is the equivalent of the Lorentz Transform when the metric is not Minkowski? How do you do a coordinate transform with a metric that has non-diagonal terms?
I wasn't quite sure where to post this, as it isn't really a homework question. My professor is teaching us General Relativity from a post-grad book, and I don't have a lot of linear algebra under my belt. He lent me the textbook he's teaching from the other day, and I got stuck when I got to...
I agree, I find that confusing as well. The Coriolis effect (Which was the frictional force i was talking about, by the way) would not contribute to a centripetal acceleration. It would always be perpendicular to the centripetal acceleration caused by the combination of gravity and the normal...
It has acceleration in two different directions. The first is the result of the Earth's gravity. It pulls the car down toward the center of the Earth, so it keeps the car on the surface of the Earth. This one is centripetal The second one moves the car along with the Earth's surface because...