Recent content by jmz34

  1. J

    Graduate Slightly confused about embedding picture and imagining spacetime

    I'm slightly confused as to how we can use the picture of a 2D surface embedded in 3D space as an analogue to understand (maybe not picture!) 4D spacetime. My initial thinking was that trying to imagine a 4D spacetime isn't really possible, it's just a mathematical concept which one should not...
  2. J

    Graduate How Does the Grand Partition Function Apply to Electron Occupancy in Defects?

    The example which I'll use to illustrate my problem is not a homework question but something I've found in a book and already know the answer to. The grand partition function, G, is defined as SUM(over i)[exp(-B(Ei-yNi))] where B=1/kT, y is the chemical potential and Ei is the energy of the...
  3. J

    Graduate QED as a gauge invariant theory

    Quick question, if there are n Feynman diagrams possible at first order say, is the rate proportional to n^2? I would have thought so since the matrix element is given by the expression M=M1+M2+M3+... where 1,2 and 3 are the consecutive orders. I've been looking at a few examples that say the...
  4. J

    Graduate QED as a gauge invariant theory

    OK that makes sense, thanks.
  5. J

    Graduate QED as a gauge invariant theory

    For the process (e+)(e-)->photon + photon the simplest Feynman diagram is just half of what you've drawn, but I'm confused about the propagator. I initially joined the two vertices for the above process with a line propagator (with no arrow) but in your diagram you have included arrows. I...
  6. J

    Graduate QED as a gauge invariant theory

    But a photon has an EM field? So is what I said about the electron interacting with the EM field correct?
  7. J

    Graduate QED as a gauge invariant theory

    I'm just beginning to learn about Feynman diagrams and wanted to make sure I've got the correct basic understanding of QED. This is what I believe to be true right now: QED allows us to describe the interaction between an EM field and light/matter. The QED vertex is composed of a photon and...
  8. J

    Coupled nuclear decay rate equations

    Homework Statement If we have the following partial decay chain: N1 -> N2 -> N3 where N1 is the number of nuclei of species 1, etc. and N1 -> N2, not via a decay but by the reaction such as N1 + neutron -> N2 + photon and we know this rate of formation of N2, say 'a'. I then get the...
  9. J

    Graduate Coupled nuclear decay rate equations

    If we have the following partial decay chain: N1 -> N2 -> N3 where N1 is the number of nuclei of species 1, etc. and N1 -> N2, not via a decay but by the reaction such as N1 + neutron -> N2 + photon and we know this rate of formation of N2, say 'a'. I then get the following rate...
  10. J

    Inhomogeneous second order ODE with non-constant coefficient

    Thanks a lot for your help. The question does say that Psi varies over a length scale that is approximately the same as the region which I'm supposed to be analyzing. Does that somehow mean I can take the RHS as constant?
  11. J

    Inhomogeneous second order ODE with non-constant coefficient

    I was trying to solve del^2(Psi)=Ae^(Psi) in spherical polars, for the radial component. Checking over my algebra I'm pretty sure it's correct.
  12. J

    Acceleration as a function of position, and time taken to travel a distance

    Using this method I did this: d/dt(0.5*(r')^2)=(-GM/r^2)r' then integrated once and simplified to get (dr/dt)^2=2GM/r solving this for t gives: t=(1/3)*SQRT(2/GM)*Ro^(3/2) If you could have a quick look at my method I'd be very grateful. Thanks a lot.
  13. J

    Inhomogeneous second order ODE with non-constant coefficient

    Homework Statement Solve ODE of form y''+(2/x)y'=C*(e^y) where C is a constant Homework Equations The Attempt at a Solution I don't really see how to approach this one, so a point in the right direction would be great. Thanks,
  14. J

    Acceleration as a function of position, and time taken to travel a distance

    I've been doing a problem that requires me to find the time taken to travel a certain distance if I know the initial acceleration of a body at the starting position and its initial velocity (starts from rest). The acceleration is a function of position a=-GM/(Ro^2). So say a body is released...