As far as I can tell, it's basically a mathematical question - you need to find the number of combinations of integers n1 and n2 such that n12 + n22 = 65 * 2 (I think the 2 should be there since for the ground state energy n1 = n2 = 1).
*facepalm* Of course, that at least makes the angular part of the integral simple. After the angular integral I ended up with:
$$\frac{2}{k}\int \frac{r\sin2\pi kr}{1+r^2}\,dr$$
I don't think this is integrable, but that makes sense based on the way the question was posed.I think it ought to be...
Homework Statement
Calculate the Fourier transform of f(x) = (1 + |x|2)-1, x\inℝ3
The attempt at a solution
As far as I can tell, the integral we are supposed to set up is:
Mod note: Fixed your equation. You don't want to mix equation-writing methods. Just stick to LaTeX.
$$\int...
I wasn't familiar with Wilson's theorem (I last did number theory more than 2 years ago, and I haven't used it since) but from what I can see it tells you that 18! is congruent to -1 mod 19. 18! = 18 * 17!, so I believe you can use this to simplify 17!.
You've probably already had your test, but everything you have done so far is correct. Now you just need to show that 1 + l(2k + 3) + l2(22k + 4) is congruent to 1 (mod 2k + 3), which it is as far as I can tell...
Right, I know that this only works because [a, b] is compact, as I stated in my first post in the thread. I believe it was you who asked how I would use this fact, which is where everything else came from.
What can you then say about |f(x) - f(y)| for any x and y that satisfy |x - y| < δ0? I never did analysis formally, but I think this is valid.
EDIT: Sorry, I very stupidly wrote sup when I meant inf in my post above, so obviously it made no sense - way too tired to be useful. I'll go back and...
Yes, the question is entirely clear. I'm frankly having a hard time believing that you are (presumably) at least a week or so into a university-level number theory course and you cannot show that (p - 1) is congruent to -1 (mod p), unless you're just having silly moment. Think about the...
Exactly... if you (the OP) don't mind my asking, what level (middle school, high school, university) is the course you are taking? It seems like you don't have a clear understanding of congruence yet, but have somehow gotten to Fermat's little theorem... it seems strange to me.