I am readind about Heisenberg's Uncertainty Principle and although the main formula most texts use is

$$\Delta x\Delta p_{x}\geq \frac{\hbar}{2}$$

or equivalently

$$\Delta x\Delta p_{x}\geq \frac{h}{4\pi}$$

I have seen it written as

$$\Delta x\Delta p_{x}\geq \hbar$$


$$\Delta x\Delta p_{x}\geq h$$

First of all, are all those correct formulas? If so, then how are they equivalent with each other?

  • $\begingroup$ Well if the first statement is true then, logically speaking, all the other statements are true. $\endgroup$ – Harshit Joshi Jan 12 '19 at 16:55
  • $\begingroup$ In my textbook, it was mentioned that the error is of the order of $h$, however on more rigorous treatment, the $\dfrac{h}{4\pi}$ factor comes into place. $\endgroup$ – Harshit Joshi Jan 12 '19 at 16:57
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/69604/2451 and links therein. $\endgroup$ – Qmechanic Jan 12 '19 at 17:52