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My professor wrote this on the blackboard:

$$\Delta E\Delta t \leq \hbar$$

Isn't the $\leq$ sign wrong? Or is this "another" possible formulation of Heisenberg's uncertainty principle?

I am at the very beginning of quantum mechanics, so I am basically not aware of anything-ish. Except for the fact that every note and book I have read so far, mention the principle with $\geq$, no matter if $\Delta E \Delta t$ or with $\Delta x \Delta p$.

Peter Mortensen
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Heidegger
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    Yes, I think that your professor made a simple typo. – Apoorv Potnis May 28 '22 at 18:12
  • @ApoorvPotnis Thank you for the confirmation! – Heidegger May 28 '22 at 18:14
  • See https://physics.stackexchange.com/q/53802/36194 as to the interpretation since $t$ is not an observable in QM. – ZeroTheHero May 28 '22 at 18:38
  • What reason did the professor give for this inequality, did the reason make sense to you, and if not, what is the conceptual issue that's troubling you? If the professor had written the name of the course as PHSYICS 101, would you be posting to ask if this is a typo, or would you be figuring this out for yourself? – WillO May 29 '22 at 04:12
  • @WillO well said. A simple search would turn up the correct inequality so unless there is some special context to write it wrong it takes all of 2 minutes to realize it’s a typo. – ZeroTheHero May 29 '22 at 12:28
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    I’m voting to close this question because it arises from a simple typo in a particular source and is unlikely to be useful to future users. – Michael Seifert May 29 '22 at 15:46
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    Ask professor what he meant. This inequality is not very meaningful without explaining what $\Delta t$ is; $\Delta E$ is presumably uncertainty in energy $E$, but time coordinate $t$ usually does not have uncertainty in QT, it is treated as independent variable/parameter. – Ján Lalinský Jun 01 '22 at 18:16

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Don't be confused. It is definitely $$\Delta E \Delta t \geq \frac{\hbar}{2}$$.

Your professor typo'd here, as if what he wrote: Then we could measure energy with any arbitrarily small error. We want to break the uncertainty principle and quantum mechanics, so it is $\geq$. We don’t want the error to be smaller than something, so it must be $\geq$, not $\leq$.

Peter Mortensen
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Abhiram Cherukupalli
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