What is Heisenberg's Uncertainty Principle?

[clementc]

What is Heisenberg's Uncertainty Principle??

Homework Statement

Hey everyone,

Until very recently, I had always thought that Heisenberg's uncertainty principle was that
$$\Delta x \Delta p \geq \frac{h}{2\pi}$$ (or $$\hbar$$)

However, I'm doing my final year of high school physics this year, and my physics teacher, tutor, random textbooks and even Wikipedia say its $$\Delta x \Delta p \geq \frac{h}{4\pi}$$.
(Well Wikipedia also says its $$\Delta x \Delta p \geq h$$ so yeah...LOL)

I was just wondering which one was really correct. I'm thinking $$\frac{h}{2\pi}$$ like it says in Giancoli and Halliday/Resnick? But not really sure.

Thank you =D

 

[0ddbio]

Well every textbook I have seen it in says that it is:
$$\frac{\hbar}{2}$$
which is equivalent to:
$$\frac{h}{4\pi}$$

Perhaps others could shed some light on why you may see it displayed different ways in different situations... But, as far as I know this is the actual formula. and it is really the standard deviations of x and p, written like:
$$\sigma_{x}\sigma_{p}\geq\frac{1}{2}\hbar$$

 

[SteamKing]

Well, Heisenberg's Uncertainty Principle strikes again!