Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

I am reading an article about uncertainty principle. If we consider a Gaussian wave packet which standard deviation of momentum ##\sigma_p##. The uncertainty principle states that the multiplication of variance of x and variance of p is larger or equal to half ##\hbar##

##\Delta x\Delta p \geq \dfrac{\hbar}{2}##

I think ##\Delta x## has the unit of meter, ##\Delta p## has the unit of kg.meter/second, so the multiplication of them give the same unit of ##\hbar##.

But if we have the Gaussian wave packet, the standard deviation of ##\sigma_x## and ##\sigma_p## should have the unit of meter and kg.meter/second. But reading the expression of variance for Gaussian given by standard deviation

##

\Delta x = \sigma_x^2, \Delta p = \sigma_p^2

##

So the unit for ##\Delta x \Delta p ## becomes kg*meter^4/second^2 ? I am confusing what mistakes I made here.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# About uncertainty principle

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**