# Evolution of wave function

1. Feb 3, 2012

### dirac68

1. The problem statement, all variables and given/known data

Hi, i would to resolve this problem of quantum mechanics.

I have hamiltonian operator of a unidimensional system:

$\hat{H}={\hat{p}^2 \over 2 m}-F\hat{x}$

where m and F are costant; the state is described by the function wave at t=0

$\psi (x, t=0)=A e ^{-x^2-x}$

where A is a costant.

How can I calculate the the avarage of x and p at time t after t=0 ( so $<x>_t$ and $<p>_t$ )?

what is the fast procedure to solve it?

2. Relevant equations
$\hat{H}={\hat{p}\over 2 m}-F\hat{x}$

$\psi (x, t=0)=A e ^{-x^2-x}$

3. The attempt at a solution

I found a solution but it seems very long and boring...

Last edited: Feb 3, 2012
2. Feb 3, 2012

### Simon Bridge

$$\psi(x,t)=\psi(x,0)e^{-iEt/\hbar}$$... where E is given by: $$\hat{H}\psi=E\psi$$

note: shouldn't the momentum operator appear squared in that hamiltonian?

3. Feb 3, 2012

### dirac68

oh yes it's p2/2m... but find eigenvalue E is too hard!

4. Feb 3, 2012

### vela

Staff Emeritus
Use the Ehrenfest theorem.

5. Feb 3, 2012

### Simon Bridge

Ahhh yes - that's easier.

You don't have discrete E eigenvalues because you don't have a lower bound - but you don't need them. Sorry, my bad.