Question

Uncertainty in position and momentum are equal. What is uncertainty in velocity?

Answer 1

According to Heisenberg's uncertainty principle,

$\Delta x\Delta p=\frac{h}{4\pi }$

As per the given condition,

$\Delta x=\Delta p=m\Delta v$

${\Delta v}^2=\frac{h}{m^{2}4\pi }$

Therefore,

$\Delta v=\frac{1}{2m}\sqrt{\frac{h}{\pi }}$