{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

$$\Delta$$x$$\Delta$$k>1

solutionish...

sin $$\frac{kx}{x}$$ = sin ($$\pm$$$$\Delta$$x$$\Delta$$k) = 0

hence $$\Delta$$x 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!