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

Can someone explain what a propagator is and does?

  1. Nov 4, 2011 #1
    So, Shankar in his famous book started to use the propagator a bunch of times in his Simple Problems in One Dimension chapter, and I have been confused to what it is and does.
  2. jcsd
  3. Nov 5, 2011 #2
    A propagator propagates :biggrin:, for instance a quantum state from time t1 to time t2.
  4. Nov 5, 2011 #3


    User Avatar
    Science Advisor

    I recommend Sakurai's book for some nice descriptive views on the non-relativistic propagator.

    Starting from the abstract Hilbert space formalism, it may be helpful to write down a few equivalent expressions for the propagator: <x'|U(t2-t1)|x> = <x'|U+(t2)U(t1)|x> = <ψ'(t2)|ψ(t1)>

    So you take a state |x>, let it evolve unitarily from initial time t1 to final time t2 and ask "what's the probability (amplitude) to find it in state |x'>".
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook