Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

In quantum mechanics, is there an upper bound for the uncertainty principle? I know that quantum harmonic oscillator (QHO) has the uncertainty relation $\sigma_x\sigma_p = \hbar(n+1/2)$, but I think the QHO becomes localized at two peaks spread out over a large distance?

share|improve this question

1 Answer 1

up vote 2 down vote accepted

When you have two operators $\hat{A}, \hat{B}$ satisfying equation $[\hat{A}, \hat{B}] = \imath \hat{C}$, you can prove with Schwarz inequality that $\sigma_{\hat{A}, \psi} \sigma_{\hat{B}, \psi} \geq \frac{1}{2} | \hat{C} |$. Unless there would be stronger inequality that can be used in calculations, it gives us the lower bound of uncertainty principle.

There is no upper bound, but if you want, you can get bigger uncertainty by lowering the trueness or precision of measurement.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.