# Uncertainty Principle textbook equation

1. Aug 23, 2013

### Daniel1992

I have been going through my Physics text book to brush up on my Quantum Mechanics before starting my next QM course next academic year and the Heisenberg uncertainty principle for position and momentum is written as ΔxΔp ≥ h-bar when I thought it was ΔxΔp ≥ (h-bar)/2. Other sources say it is the latter so am I missing something? Or is the text book just wrong?

2. Aug 23, 2013

The latter (hbar/2), assuming that Δx and Δp are interpreted as standard deviations from their respective means.

3. Aug 23, 2013

### Daniel1992

So are there circumstances when ΔxΔp ≥ h-bar is correct? Say when you are not dealing with standard deviations?

4. Aug 23, 2013

### Staff: Mentor

When you're interested mainly in order-of-magnitude estimates (powers of ten), a factor of 2 or 1/2 or something like that doesn't affect the result significantly.

5. Aug 23, 2013

### vanhees71

The correct Heisenberg-Robertson uncertainty relation is
$$\Delta x \Delta p \geq \frac{\hbar}{2}.$$
You can show that the Gaussian wave packets are the only ones, where the equality sign is valid.

6. Aug 27, 2013

### Daniel1992

OK, thanks for clearing that up.