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Tor Fredrik

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About Tor Fredrik

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    thermodynamic, electromagnetism and quantum mechanics

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  1. In the example 5.11 above I don't understand how they revert to the natural coordinates while going from (5.68) to (5.69). In (5.68) the direction is along the y-axis. In (5.69) it follows the angle that goes round the sphere. But this angle is normal to y when it is at the y axis and parallell to the y axis while it is at the x-axis. How is it possible to revert between the y-axis in (5.68) and the angular axis in (5.69)?
  2. I did stumble upon a thing about gauss law I guess this could explain that the sum of div of E inside the whole electron is as noted in gauss law But as for deriving without using gauss law? I think this problem in Griffiths might help I guess I just would have to read the answer properly
  3. But in the orange part in my first post in this thread they use that thet get a value for the volume integral at origo and that it is 0 everywhere else. Yes luckily I did find my table. I see now that the requirement in the proof for gauss divergence theorem was that the volume must be continuous. So they are not mentioning F. So is it possible to prove that F does not have to be continous from the fundamental theorem of calculus? For example this note might pull one in the right direction?
  4. In 5.55 they use Gauss law. In my proof of Gauss law they require that there is no holes on the volume of Gauss law. But in 5.55 there is a hole when the radius is 0. How can you create a proof for this rewriting then? I have the same issue in the electromagnetic gauss law: Then they introduce Gauss law even though the electric field E is undefined in origo I guess I in the end must add a derivation for Gauss law so that someone can point out how the proof is still valid for the theory above.
  5. they refer to a product rule 5 for the second last equality above. This text is taken from David Griffiths, introduction to electrodynamics. If anyone is familiar with the book. At what page is product rule 5 that is used here introduced? I cant find that page. Or does anyone have another book or a internet site where this product rule 5 is derived? Or does anyone want to derive the second last equality above here on this page? On a further note I understand that So I understand how they obtain the left side of:
  6. Why would that lead to that the divergence of the current density is 0. Can you show it mathematically?
  7. Above they derive that curl of B is uJ. I know they use the identity So since as underlined above that the derivatives of J is 0 we have that But my problem is why is the derivative of J 0 in general. I have looked at a derivation for this: And the end of this derivation is the following But in the derivation they use that acceleration is constant and that it is a function of E showed in the orange box above. But E does not have to be constant since it is a function of r? So how is this a general derivation for the fact that divergence of current density is 0?
  8. I have wanted to edit the post above. But since I have not managed to edit I will write an update. Further derivation for the frequency is 'so if a photon between the two mirrors are moving then we would get for the mirror that moves away from the photon As for the other mirror I am not sure. It does move away from the photon as well but (1) uses toward the source. And why are there two photons needed for this derivation? In short I am a bit lost over the energy translation here between the two mirrors and the photons. I am aware that they use p=E/c introduced by Maxwell.
  9. Thanks for all the response. I have moved on and looked at a different derivation that uses E=hf. The formula that I have derived for the doppler shift formula is for this case gives this corrected wavelength And this case gives this observed wavelength But is this applicable to the momentum formula in (1). And how do they use plancks constant h in the momentum approxiamtion to the left of (1). Can someone derive this momentum approximation if possible?
  10. I have tried to work on a derivation. Here is what I obtained. But my problem is how to get from an arbitrary velocity v to the speed of light.
  11. It does not have to be a new theorem where E=mc^2 has not been applied. But a quantification of why E=mc^2 is legit. I am pretty sure I read something about it. Could you write a list over all proofs of E=mc^2 that you know? Semi emperical and not emperical. Would be great.
  12. Albert Einstein did introduce E=mc^2 historically. I have seen numerous proofs for this relativisticly or by calculus from Newtons laws. However for some time ago I found a site that described that a scientist did prove E=mc^2 from an energetic perspective by adding together all energy available from different energy types. I can't find this site online now unfortunately. So I wonder if anyone know the name of this proof for E=mc^2 by adding together different energy contributions. I don't want a derivation I simply want a site that describes this theory or the name of the theory if it has one. It is not this wikipedia page I am looking for https://en.wikipedia.org/wiki/Mass–energy_equivalence I believe the proof was introduced a bit later then Einsteins proof perhaps later then 1930. I cant remember if it was semiemperical or not.
  13. So how do you interpretate this. For example for a normal distribution. I have an assignment about this in my textbook It would be easier if someone could show me directly how this is valid
  14. I will add the start of the theory that obtains the fisher information from the maximum likelihood function My notes from this theory is that they talk about the maximum likelihood estimator and that they introduce a sample which should be T in the theory in the first post. My question is still the same: Above they use the expected value of T where T is the estimator for example mean or median as in the example in the beginning of the question. But since they find the expected value of T must not they then use the pdf that corresponds to T? Which in the example above would be gamma and normal respectively. How can then Cramer Rao bound compare anything Just for clarification. The example in the beginning of the first post is not from the rest of the theory. The theory after the example in the first post comes just after this theory added in this post in the chapter of the theory is taken from. Thanks for the answer.
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