Recent content by Domnu

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    Cauchy Sequence That Does Not Converge In A Space

    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.
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    Could an Antimatter Bomb Match the Power of the Tsar Bomba?

    antimatter has definitely been created, but creating substantial amounts of it is difficult.
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    [Q]How can i draw real graph from complex function?

    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.
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    Clebsch Gordan Coefficients

    Problem Express \bold{S}^2 in the |j_1 j_2 ; m_1 m_2\rangle and |j_1 j_2; s m\rangle bases and find the unitary matrix, U, which takes the |j_1 j_2 ; m_1 m_2\rangle basis to the |j_1 j_2; s m\rangle basis, for spin 1/2 (s corresponds to the total angular momentum while m corresponds to the...
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    Solving Electromagnetism Questions: Charged Particles

    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...
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    Solving Electromagnetism Questions: Charged Particles

    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...
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    Solving Electromagnetism Questions: Charged Particles

    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...
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    Solving Electromagnetism Questions: Charged Particles

    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...
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    Rotation Operator/Orthogonal matrices in quantum mechanics

    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...
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    Perturbation theory energy shift for hydrogen atom

    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).
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    Rotation Operator/Orthogonal matrices in quantum mechanics

    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...
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    Time Dependent Perturbation Theory

    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...
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    Time Dependent Perturbation Theory

    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...
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    Time Dependent Perturbation Theory

    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...
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