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Matrix elements of the time development operator (position representation)

  1. Sep 28, 2011 #1
    1. The problem statement, all variables and given/known data

    There is a freely moving particle of mass m. Prove that the matrix elements of the time development operator, T(t,0), in the position representation is <q'|T|q''> = [(m/2i*pi hbar t)^1/2] Exp[-m(q'-q'')^2/2it hbar]

    2. Relevant equations

    H = (p^2)/2m

    3. The attempt at a solution

    I know that for the momentum representation:

    <p'|T|p''> = delta(p'-p'')Exp[-i(p'^2)t/2m hbar]

    And I tried starting with:

    <q'|p><p|q''> Exp[-i(p'^2)t/2m hbar]

    but I am very new to this notation, and I'm not sure where to go next.
     
    Last edited: Sep 28, 2011
  2. jcsd
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