1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Transmission amplitude using path-integrals

  1. Mar 26, 2008 #1

    As a path-integral newbie, I've been trying to calculate the amplitude for an electron which enters a box (potential within the box is given) at a point to emerge the other edge of the box (it doesn't matter when it exits). For simplicity, I first tried to work out the problem in one dimension, and in discrete space-time. To simplify it even further, I tried with a constant (but non-zero) potential.

    I worked out the kernel [tex]K(b,a)[/tex], but it -naturally- depends on time spent in the "box". But I don't care when will exit, I care only whether if it can or can not penetrate through.

    I have [tex]\psi(b,t_b) = \int K(b,a) \psi(a,t_a) da[/tex], and transmission amplitude at [tex]t_b[/tex] would be "inner product" of wavefunctions at [tex]t_b[/tex] and [tex]t_a[/tex] (but well, how? They don't have a variable in common at all! Do I get to expand the wavefunction in eigenstates of position?). So I guess, to get the total amplitiude, I get to compute the amplitude for all times after [tex]t_a[/tex], and add them all. Sounds plausible to me, but how would I do an inner product with [tex]\psi(b,t_b)[/tex] and [tex]\psi(a,t_a)[/tex]? Or am I quite off?
    Last edited: Mar 26, 2008
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted

Similar Discussions: Transmission amplitude using path-integrals
  1. Diffusion path (Replies: 1)