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  1. H

    Nothing without movement

    Too good!
  2. H

    I Acceleration through curved paths

    As I understand your problem, you are looking to solve for motion with a constraint like ##|\dot{\vec{r}}|=bt+c##. You could take a polar parametrization like ##r(t)=R_0(1+d\sin{\theta(t)})##, substitute it into the polar form of the constraint...
  3. H

    Can the Simulation Hypothesis be verified or falsified?

    Whether or not we are living in a simulation, reincarnation is real! This thread has been reborn twice! QED
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    I Are Newton's Laws of physics compatible with thermodynamics?

    What a question, haha! I will suggest another question to you that you can look into. How, given the time-symmetric equations of motion in both classical (Newton's physics) and quantum physics, can the arrow of time (thermodynamics) arise?
  5. H

    A Analytical solution for an integral in polar coordinates?

    The last integral here looks like a multiple of the complete elliptic integral of the second kind. If a special function counts as an analytical solution, then you might be in luck. As for the logarithmic integral, I'm unclear if you can even find special functions.
  6. H

    Nothing without movement

    Do you happen to know the source for the quote? I did a quick Google search and couldn't find it. People rarely proclaim a sentence or two and leave it at that---context would help. The quote is sufficiently woowoo that you could read all kinds of meaning into it.
  7. H

    Is this 2 Nobel Prizes given in a single year?

    It also strikes me as a little strange. The physics Nobel appears to be shared between work specifically done in climate science (two of the winners share half the prize for this) and work for the discovery of the interplay of disorder and fluctuations in physical systems from atomic to...
  8. H

    And the 2021 Nobel prize for Physics goes to...

    Two people share half the prize for climate models, the other half goes to Parisi. Climate is probably just a better publicity generator than "theory of disordered materials and random processes."
  9. H

    I Strange feature of BE, FD and Boltzmann distributions

    I think what makes thermodynamics seem metaphysical is the willy-nilly use of limit taking combined with the fact that thermodynamics is the subject whose sole purpose is to relate physical variables; i.e. if you take a limit here you're probably taking it for any number of other variables...
  10. H

    Physics Viability of publishing as an independent researcher

    The hard part is deciding what is "relevant" as used in the rule. The tricky part of conflicts is that it is hard to determine from the perspective of the person who may have a conflict. That means to me that you always have to lean in the direction of full disclosure. Outside of ethics, I think...
  11. H

    Physics Viability of publishing as an independent researcher

    Here are the APS ethical guidelines. Conflicts are near the end.
  12. H

    I Making Rings on the ISS

    I appreciate the explanation but I think it still ignores the issue which I believe complicates the analysis. That is, the dependence of the force/potential on the relative orientation of various vector quantities in the problem.
  13. H

    I Making Rings on the ISS

    I share the intuition of many of those who have posted about the behavior for central potentials. However, as a nitpick, I'm not entirely convinced that just because something isn't 1/r or r^2 for potential there can't be closed orbits. Bertrand's theorem is the mathematical statement of what...
  14. H

    Books that teach classical mechanics through a discourse method

    How do you distinguish the example problems solved in a standard physics textbook from what you are looking for? In general, "interesting" is not a good proxy for what will teach you the skills to solve problems yourself. Maybe the Feynman lectures would suit your purpose. They are kind of...
  15. H

    I Quantum spin, wavelength and frequency

    Just because you can find planck's constant in some expression and isolate it doesn't mean the variables on the other side of the equals sign relate to spin. If you study quantum mechanics, you will find that planck's constant appears... well... everywhere.
  16. H

    Mentor application

    You have a massive code rewrite to ensure server performance?
  17. H

    A Fidelity for quantum state at t=0

    Your substitution of ##t=0## looks fine, but you make an algebra error moving from the first to second line. Maybe you corrected the mistake later.
  18. H

    Find the eigenfunction and eigenvalues of ##\sin\frac{d}{d\phi}##

    It would probably just be an even more horrible function. In the end, you can always just define a function which is the inverse of another, but that's little more than giving something a name. Insight comes when there are known properties of the variously named special functions.
  19. H

    I Making Rings on the ISS

    This is an interesting thought experiment. Thinking of the iron filing and the magnetized sphere as two dipoles, I don't think the force between them follows an inverse-square law. There is a fun little theorem called Bertrand's theorem which tells us which kind of central potentials have...
  20. H

    Find the eigenfunction and eigenvalues of ##\sin\frac{d}{d\phi}##

    It isn't pretty and I doubt there is an expression for ##f## in terms of elementary functions, but you could just take arcsine of both sides and directly integrate.
  21. H

    A Fidelity for quantum state at t=0

    In that case, I'm with @Demystifier. We will need to see your calculations to know what's going wrong. Because if you switch the order of the kets and take ##t=0##, then you get exactly the initial state.
  22. H

    A Fidelity for quantum state at t=0

    I'm only doing math in my head, but are you sure you have the order of the kets correct in the final state? I would think you'd be able to just take ##t=0## in ##\chi## and recover the initial state.
  23. H

    Great one-liners from PF members

    Although said in the context of someone trying to do quantum mechanics without complex numbers, I also think it might make a great entry in a self-help book 😅 (something something lower case i something something taming ego something something)
  24. H

    I Uncertainty principle equation for virtual particles

    This topic is subtle and requires extremely careful consideration, as you can see from the replies you have received so far. I will add one caution to the mix: do not confuse experimental precision (uncertainty) with the uncertainty relations. The real mystery of quantum mechanics is that even...
  25. H

    What do you do when you get bored?

    One of these things is not like the other... What inspired you to even think to brute force shred a newspaper like that?
  26. H

    A Formula for this curve?

    In the event you have access to Mathematica, here is a pre-written notebook for the Hodgkin Huxley model you can fiddle with:
  27. H

    Calculating Transient Heat Transfer in Pipes with Thick Walls

    I have a general piece of advice: don't try to solve the hardest problem first. For example, the first thing you might try, just to get your feet wet, is to find the steady-state distribution in the concrete pipe, assuming the hot air is flowing forever at fixed temperature and the outside...
  28. H

    I Uniquely Defined Accelerations

    That's definitely a good instinct to have when you go through Landau, but I think in this instant he's just getting the reader primed to see how these facts fall out naturally from extremizing the action.
  29. H

    I Uniquely Defined Accelerations

    I think in this case Landau has a little more in the back of his mind. I would interpret "from experience" to mean something like all the classical forces we know depend on at most the first derivative of position. In that sense, any acceleration at a particular time is determined by the...
  30. H

    Studying Seeking your suggestions on my upcoming undergraduate course workload

    And talk to the people farther along than you are. BUT talk to multiple people before you take action based on what they say. Individual people can have eclectic views of various courses; you want to make sure to average those out by asking multiple people. Lastly, every plan should be followed...