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Path Integral Basics (Why dimension increases in the integrals?)

  1. Jan 3, 2012 #1
    Alright, I have a kind of dumb question:

    Why do I distinguish between dq and dqi when considering the propagation from qi to q to qf?

    For example, if we want the wave function at some qf and tf given qi and ti, we may write:
    ψ(qf,tf)=∫K(qftf;qiti)ψ(qi,ti)dqi

    Why do we distinguish between dqi and say, dq, of an intermediate point q?

    I understand that a second integration arises, naturally, since another propagator is defined. I just don't get the need to distinguish? I feel like it's almost book-keeping, like we write out (or don't since we use product notation followed by a script D) our dq's so we don't have to write out more integrals...

    I know that's not right though, because we treat q and qi as different things...

    Some direction would be great...I feel kind of dumb for whatever I'm missing.

    edit:
    I think I mis-titled this a little, but it's close enough, I hope.
     
  2. jcsd
  3. Jan 4, 2012 #2
    I'm not quite sure what you're asking but when deriving path integrals one takes the propagation (or the sum of all propagations) between states i and f and subdivides them, and then subdivides them again, and again until the path between two states has been turned from a finite path in phase space to an infinite sum of infinitesimal paths.
     
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