Recent content by Domnu

Consider the sequence 1, 1/2, 1/3, ... in the space X = R \ {0}. This is a Cauchy sequence in X which does not converge in X.

antimatter has definitely been created, but creating substantial amounts of it is difficult.

In addition, you could plot 3D graph as follows: let the x coordinate be the real part of the input, let the y coordinate be the complex part of the input, and let z be the magnitude of the output. You can change this around to get the complex part of the output, etc.

Yes, I arrived at the same answer as Besh. It is true that my answer is a bit complicated; this is why I am not completely sure. If this was an exam taken from a high school Physics C course or introductory physics course in a university, then my answer would be a bit too much, but then if it...

You're welcome :smile:

I just read part V, and I think the answer is (C). Here is my reasoning (I may be overthinking the problem, but this is true): the problem doesn't state that the current is *immediately* steady, but is *quickly* steady. From this, we can observe that the voltage must increase from 0 to V at a...

Okay, so it looks like you got the first question right. Good job! :smile: For the next part, try to use Gauss's Law. If you haven't heard of this, then never mind... just know that whenever you have a conducting surface, the charge distributes itself over the surface such that *the net electric...

Hello Billy246 :smile: Well i) is simple if you just use V = kq/r, or 1/(4pi epsilon) * q/r, whichever notation you like. Now, you got ii) right, but can you prove your answer? (Hint: use Gauss's Law) Try looking at iii) again... does it HAVE to be at 0 potential? I'll take a look at the rest...

Right, so we can try to do something of the following form: let A be our matrix such that A = \begin{bmatrix} a & b & c\\ d & e & f \\ g & h & j\end{bmatrix} Now, each of the columns are orthogonal to each other, and we need that the determinant of A be 1. In addition, we know that the...

Hello Philip041 :smile: Could you describe what delK is? From what I can see, this looks like the first order relativistic correction to the hydrogen atom, commonly found in the fine structure correction (minus the spin orbit coupling).

Hello Vivek :smile: All you have to do is to show that any orthogonal matrix can be interpreted as a rotation matrix. While you have stated that all rotation matrices are orthogonal, you have to show that all orthogonal matrices can be seen as some sort of rotation matrix. Now, if you can do...

Happy New Year's Eve! :smile: Ah, okay. I think I see what you're doing now. To be honest, I haven't seen that formula before. Could you explain exactly what the formula is? I know that to find the first order energies, you would do \langle \psi | \text{perturbation} | \psi \rangle where \psi...

Well, the first part is correct. Now, the second part is correct, but when you say you have to work out the matrix element, could you say exactly what you mean? I'm pretty sure you're on the right track. I could give you a hint: remember that \langle \alpha | \beta \rangle is the probability...

You're very welcome! Well, you got the first part, so nice job! :smile: Aaaah! You're trying too much for the second part.. you could try working it out a bit easier.. if you're familiar with bra-ket notation, you could try working something out where you have \psi, our initial ground state ket...

Hello wam mi :smile: This problem is not actually a time dependent perturbation theory problem; it is, in fact, a time independent perturbation theory problem, because the potential doesn't change with time. If the particle is in the ground state for t < 0 and there is NO perturbation, what...