Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Bound states in propagator

  1. Oct 13, 2012 #1
    Why must it be true that a system that has a bound state must have its scattering amplitude have a pole in the upper half of the complex wave-number plane?

    For example, if the scattering amplitude as a function of the initial wave number magnitude |k| is:

    with B>0, then there is a pole at k=iB which implies the energy is:


    that is, a negative energy or bound state.

    But if B is negative, then the pole is at k=-i|B| and the energy would be the same using the same formula, but this doesn't represent a bound state because for some reason the pole must be in the upper-half of the complex plane. Why is this true?
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted