# Free particle <p>

1. Jan 30, 2014

1. The problem statement, all variables and given/known data
A free particle moving in one dimension is in the initial state ψ(x,0). Prove that
<p> is constant in time by direct calculation (i.e., without recourse to the
commutator theorem regarding constants of the motion).

2. Relevant equations

<p> = m*(d<x>/dt) ?
S.E.
ψ(x,0)= 1/(√(2∏))*∫Θ(k)e^(ikx)dk

3. The attempt at a solution

I am not really sure where to start... Should I find <x> ? is that the easiest way? And how do you this for a free particle ? stuff is confusing me. Can someone give me a start here...

2. Jan 30, 2014

### vela

Staff Emeritus
No, don't use this. Use the definition of the expectation value of an operator.

What is the Hamiltonian for a free particle?