Uncertainty Principle textbook equation

[Daniel1992]

I have been going through my Physics textbook 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 textbook just wrong?

 

[gadong]

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

 

[Daniel1992]

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

 

[jtbell]

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.

 

[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.

 

[Daniel1992]

OK, thanks for clearing that up.