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  1. J

    Numerical Plot of Particle Orbits in Kerr Equatorial Plane

    I don't know. But it occurs to me that conservation of energy might be a problem. The only cases of spiral orbits I can think of immediately involve some change of orbital energy--drag from viscous forces, emission of gravitational waves or absorption of electromagnetic energy as in a cyclotron.
  2. J

    Numerical Plot of Particle Orbits in Kerr Equatorial Plane

    Not that's obvious to me. But it might be worth trying to narrow the range of possibilities first. Are you sure that spiral orbits are possible? Are there stable closed orbits in the Kerr metric? If so, it might be worth starting from one of those and trying to perturb it. ( Perhaps replace r...
  3. J

    Numerical Plot of Particle Orbits in Kerr Equatorial Plane

    Did you consider what relations between r and φ would give you a spiral and going from there?
  4. J

    Transmission for double delta-potential vs single delta

    I suspect this is a strong hint. Is there a relation between the separation of the two deltas and the wavelength of the wave-function?
  5. J

    Occupancies in sub bands of a quantum well

    I think it may be. Depends what "it" is, of course.
  6. J

    Occupancies in sub bands of a quantum well

    Perhaps the way to think about this question is to imagine the hypothetical well with one sub-band as a kind of "bucket" that would have been filled with electrons to a "depth" of 50 meV. (This seems to explain why the occupancy is expressed in meV.) How would you picture the real well in those...
  7. J

    Occupancies in sub bands of a quantum well

    As I understand it, the total energy is the fermi energy you have the equation for, plus the potential energy referred to some chosen zero level. I think it might be useful to draw an energy-level diagram comparing the assumed quantum well with one sub-band and the real well with two sub-bands.
  8. J

    Occupancies in sub bands of a quantum well

    That sounds promising. Do you understand why the occupancies are apparently measured in meV? I admit that's not clear to me.
  9. J

    Occupancies in sub bands of a quantum well

    Do you know of a relation between the energy of the system and the number of levels that are occupied?
  10. J

    Occupancies in sub bands of a quantum well

    What do you understand by "occupancy"? I think your list of relevant equations is incomplete.
  11. J

    Using perturbation to calculate first order correction

    Is your integral in section 1 missing a factor of 4π? In the first equation in section 3 I think you've lost the factor of 2 from each Rnl(r). And when you put in the limits of integration, the exponents in your final equation should be -2b/a0. It's not clear to me what the perturbation is...
  12. J

    How do I use this equation? Estimating half-life of a decay

    I found this useful: /instruct/ch374/ch418518/Chapter%207%20Alpha%20Decay-rev.pdf Equation (8.18) seems to give a reasonable answer for alpha decay (rough calculation, not checked). The factor in front of the exponential is very small and may reduce the product to the right level. I'd try...
  13. J

    How do I use this equation? Estimating half-life of a decay

    After a bit more reading I find that the only listed decay processes for 220Th are electron capture, and alpha decay with a half-life of about 10 μs. See Wikpedia, "Isotopes of Thorium". Edit: Not sure if the much slower 12C process would simply be ignored in the listings, if it''s real, or if...
  14. J

    How do I use this equation? Estimating half-life of a decay

    After a tiny bit of reading, I gather that 12C decay might be rather slow. What it look like if you just calculated ln (t1/2) ? Edit: ignore this--you're trying to compare with a calculated result.
  15. J

    How do I use this equation? Estimating half-life of a decay

    Do you know if the equation does in fact give a reasonable answer for alpha-decay?
  16. J

    How do I use this equation? Estimating half-life of a decay

    I just noticed that eq. (8.18) is for alpha-decay, not 12C decay; does that make a difference?
  17. J

    How do I use this equation? Estimating half-life of a decay

    Can you pin down which is the big number? For instance, the text above equation (8.18) indicates that x = Q/B should be << 1. Is it?
  18. J

    Conserved quantities in the Korteweg-de Vries equation

    I don't think you should have the factor of c outside the integral, but you need a factor of d in the last term of the integrand. (But I'm also one of those that deplore using d as a constant in anything involving calculus.) It looks as though the integrand should be expressible in terms of an...
  19. J

    Hydrogen atom in a magnetic field

    The magnetic moment of the proton is much smaller than that of the electron. But the angular momentum of any spin-1/2 particle can take up one of two orientation is a magnetic field.
  20. J

    I'm stuck on solving a linear quadrupole problem

    For part (a) I wonder if you were expected to do simple electrostatics and geometry--adding up the single-particle fields, and doing first-order calculations for the distances. (I note that in your derivation you didn't insert the unit vectors until the last steps, so technically you're equating...
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