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  1. H

    Conditional probability of several events? (sports-related)

    I'm casually working on determining the probability of a team in a given sport (let's say football) reaching at least a certain level in a season. There are two main parts to this: How many games they won in the season, and how far they got in the playoffs. I'd like to assign one final number...
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    Trying to understand the oscillation of electrons in the magnetic fiel

    Yes, but what is the physics behind the reduction in the parallel component? Why does it reduce? I found this, which explains it well in terms of a dipole, but perhaps there's an explanation in terms of just the particle?
  3. H

    Trying to understand the oscillation of electrons in the magnetic fiel

    Yes, this makes sense, and I know I can think of it either as purely magnetic (Earth's frame) or as an electric field (electron's frame). I thought the electron's frame would be easier but it hasn't been. Then to me it seems that perhaps the converging of the magnetic field lines might help...
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    Trying to understand the oscillation of electrons in the magnetic fiel

    Working on understanding the physics of how an electron oscillates along the Earth's magnetic field. I understand that an electron will spiral around the magnetic field line, that's easy to tell from the Lorentz force. What I don't understand is what causes the oscillation. My best guess is...
  5. H

    A continuous function having an inverse <=> conditions on a derivative?

    Sorry for the poorly-worded title. I help tutor kids with pre-calculus, and they're working inverse functions now. They use the "horizontal line test" to see if a function will have an inverse or not by seeing visually if it's one-to-one. I was thinking about what that might imply. If a...
  6. H

    Covariance between x and f(x)?

    Homework Statement As part of an assignment, I have to determine propagated error of some function: f(x,t) I did it first with x & t being completely uncorrelated, but now I'm given x as a function of t, x(t), and have to do the same. Homework Equations I know the linear approximation for...
  7. H

    How to evaluate this integral to get pi^2/6:

    Anyone else have any input?
  8. H

    How to evaluate this integral to get pi^2/6:

    \int_0^\infty \frac{u}{e^u - 1} I know that this integral is \frac{\pi^2}{6}, just from having seen it before, but I'm not really sure if I can evaluate it directly to show that. I know that: \zeta(x) = \frac{1}{\Gamma(x)} \int_0^\infty \frac{u^{x-1}}{e^u -1} du Does the value...
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    Proving that 'volume' and 'surface' of hypersphere go to 0 as n -> infinity?

    Homework Statement I'm supposed to find the equations of a hypersphere in n-dimensions (meaning the set of points within the radius R), as well as of its surface (the set of points at exactly radius R). I've already found the equations, and now need to show that both go to zero as n goes to...
  10. H

    Perturbation with equations of motion for air resistance

    Homework Statement "A ball is tossed upwards with speed V_0. Air resistance is -mkv^2 and there's gravity too. Find the the time it takes the ball to reach the maximum height. Do not solve the equation of motion exactly. Use the perturbation method on the equation of motion. Solve the equation...
  11. H

    Estimate mass of neutrino given distance & KE

    Homework Statement A supernova 1.54\times10^21 m away sends out neutrinos, and a detector on Earth detects two, ten seconds apart. The first one (A) that comes has a kinetic energy of 30 MeV, the second (B) has a kinetic energy of 10 MeV. Using this, I'm supposed to come up with an upper...
  12. H

    Finding total energy as a function of the Fermi Energy

    OH I get it -- that clears it up a lot. Thanks! I was able to get it from there, I really appreciate the help!
  13. H

    Finding total energy as a function of the Fermi Energy

    Hmm actually I'm still having some trouble with this one. I get why you can integrate from 0 to E_{Fermi}, yet I'm not following when you plug in the equation for E_{Fermi}. Did you do it before or after integrating? If before, I keep getting to an integral I can't solve: \int_{0}^{E_{F}} \...
  14. H

    Finding total energy as a function of the Fermi Energy

    Yeah this is the Harris problem haha. So I plug in the Fermi energy equation for E in the top, as well as N(E)_{FD} and D(E)? Sounds good, I'll try it and see where it gets me. Thanks, I was just leaving the term as E and it wasn't working too well
  15. H

    Finding total energy as a function of the Fermi Energy

    Homework Statement "The numerator of this fraction: \overline{E}=\frac{\int \! E N(E)D(E)dE}{\int \! N(E)D(E)dE} (N(E) is the number of particles in an energy state, D(E) is the density of states) is the total (as opposed to the average particle) energy, which we'll call U_{total} here...
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    For what Z values does an atom begin to differ from a nonrelativistic model?

    Awesome thanks! That helped a lot -- that was a much simpler problem than I was making it in my head. Thanks again, good luck on tomorrows quiz, haha
  17. H

    For what Z values does an atom begin to differ from a nonrelativistic model?

    Homework Statement "Relativistic effects are rather small in the hydrogen atom, but not so in higher-Z atoms. Estimate at what value of Z relativistic effects might alter energies by about a percent and whether it applies equally to all orbiting electrons or to some more than others. For this...
  18. H

    Finding all of the right cosets of H in G

    Ahh, so the negative powers cycle through as well. Okay thanks! That helps a lot!
  19. H

    Finding all of the right cosets of H in G

    Okay awesome, thank you very much. I guess what I'm confused about is that the definition for a cyclic group said, {a^i | i=0,-1,1,-2,2...}. Here, we only used the positive values of i, and I guess I'm unclear as to why we did that.
  20. H

    Finding all of the right cosets of H in G

    Ahh right. So would it be: H = {a^0, a^2, a^4, a^6, a^8}? Then that leads me to infer that the other right coset must be: {a^1, a^3, a^5, a^7, a^9} But I'm not sure how quite to show that -- is it because the first coset is He, where it's acting on the identity, and the other one is Ha, where...
  21. H

    Finding all of the right cosets of H in G

    Then that makes H = G, doesn't it? H = {a^0, a^3, a^6, a^9, a^2, a^5, a^8, a^1, a^4, a^7}, if I keep adding 3 to the powers and cycling through once they get to ten. Then it's clear that H = G.
  22. H

    Finding all of the right cosets of H in G

    Homework Statement "Write out all the right cosets of H in G where G = (a) is a cyclic group of order 10 and H = (a^2) is the subgroup of G generated by a^2." Homework Equations - If G = (a), then G = {a^i | i=0,-1,1,-2,2...}. - A right coset is the set Hb = {hb | h is in H} - Order of...
  23. H

    Find the limit using Maclaurin series:

    Yeah, but that didn't seem to help. I'm left with a jumble of series and not really sure where to go from there. It says to take the first term of both numerator and denominator, but given that the denominator is the square of the series (and that the first term is zero), I'm not really sure...
  24. H

    Find the limit using Maclaurin series:

    Homework Statement \lim_{x\to0}[\frac{1}{x^2} - \frac{\cos(x)}{\sin(x)^2}] I'm supposed to use Maclaurin series to evaluate this limit. The instructions suggest, as a hint: "First combine the fractions. Then find the first term of the denominator series and the first term of the numerator...
  25. H

    Which momenta can never be measured?

    The class I'm taking doesn't expect us to use Fourier transformations yet, is there another way of looking at this?
  26. H

    Which momenta can never be measured?

    Homework Statement "A particle is described by: \psi(x) = \left\{ \begin{array}{lr} C & : \left|x\right| \leq +\frac{1}{2w}\\ 0 & : \left|x\right| > \frac{1}{2w} \end{array} \right. What momenta can never be measured?" Homework Equations \Delta p...
  27. H

    Range of wavelengths from a laser pulse?

    hmmm and this time I did get that, I must've plugged it into Mathematica wrong. Thank you for your help! :]
  28. H

    Range of wavelengths from a laser pulse?

    Hmm, so I gave that a try: \Delta \omega \Delta t \geq \frac{1}{2} \delta (\omega )= \delta ( 2 \pi f) \delta \omega = 2 \pi \frac{-c}{\lambda^2} \delta \lambda Then, if I solve that for d(lambda), and plug everything in, I get about .95 um, which is an order of magnitude higher than what I...
  29. H

    Range of wavelengths from a laser pulse?

    Homework Statement "A 1 fs pulse of laser light would be 0.3 um long. What is the range of wavelengths in a 0.3 um long pulse of (approximately) 600nm laser light?" Homework Equations (delta omega)(delta t) >= 1/2 c = (lambda)(frequency) The Attempt at a Solution I replaced (delta...
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