- #1
cleggy
- 29
- 0
Homework Statement
Use the generalized Ehrenfest theorem to show that any free particle with the one-dimensional Hamiltonian operator
H= p^2/2m obeys
d^2<x^2> / dt^2 = (2/m)<p^2>,
Homework Equations
The commutation relation xp - px = ih(bar)
The Attempt at a Solution
d^2<x^2> / dt^2 = (1/m)(d<p^2>/dt)
H = p^2/2m + V(x)
then [x^2,H] = x^2[(p^2/2m) + V(x)) - ((p^2/2m) + V(x))x^2 = (1/2m)[x^2,p^2]
[x^2,p^2] = xxpp - ppxx = 2ih(bar)(xp + px)
I'm stuck at this point?
am i on the right track?
the < > brackets represent the expectation value