{Uncertainty Principal} Uncertainty in position and wave-vector

[Liquidmoose]

A Wave packet is described by

\Psi(x)= sin \frac{kx}{x}

Make reasonable estimates of the uncertainty in position and wavevector and show that this function obeys the uncertainty priciple

\Deltax\Deltak>1

solutionish...

sin \frac{kx}{x} = sin (\pm\Deltax\Deltak) = 0

hence \Deltax must = some interger of \pi...?

this is about where i get lost don't know if I'm going in the right direction!?

 

[jae05]

isn't \sin{\frac{kx}{x}}=\sin{k}? do you mean {\frac{\sin{kx}}{x}} instead?

 

[Liquidmoose]

yeah ta!