# Dispersion in for a free particle

1. Sep 29, 2011

### marcelnv

Hey,
I am trying to calculate the dispersions $\Delta$P and $\Delta$X for a free particle with definite momentum $\Phi$(x) = Aexp(ikx) where A is a normalization constant. This i get
$\Delta$P = 0
$\Delta$X = $\infty$
What physical interpretation can I give to these results? Is is that the momentum is well specified and can always be obtained with certainty and that the position can be anywhere?
Also,
I am trying to solve the same problem for a free particle in the state
$\Phi$(x) = A*Cos(kx).
I get integrals involving sin and cos to be evaluated at $\infty$. Using taylor expansion, i argue that
$\Delta$P = $\infty$
$\Delta$X = $\infty$

Am I correct?
The function $\Phi$(x) = A*Cos(kx) seems not to be normalizable to me, so should not be used to represent the state of a quantum mechanical system. What do you think?

Thanks

Marcel