# Matrix elements of the time development operator (position representation)

1. Sep 28, 2011

### siritachi

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