Is there a Typo for the Generalized Uncertainty Principle in Griffiths Quantum Mechanics Fundamental Formulas?

Question

I was memorizing the "Fundamental Formulas" inside Griffiths’ book cover (ISBN: 0131244051) for an upcoming test but I noticed that if I plugged x and p into the "Generalized Uncertainty Principle", using the "Canonical Commutator", then the result I got didn’t match the given "Heisenberg Uncertainty Principle". The righthand side was squared and looked like it shouldn’t have been.

Generalized Uncertainty Principle inside book cover

So I looked through the book for where he talked about the Generalized Uncertainty Principle and found it on page 109 (Eq. 3.137), and it looked like it didn't match the generalized uncertainty principle inside the cover. I think the LHS of the inequality in the cover should be squared (or the RHS shouldn't be).

Am I missing something, or is it a typo?

rob · Answer

Since $A$ and $sigma_A$ have the same units, an equation with $A^2$ on one side and $sigma_A$ on the other is probably dimensionally inconsistent. The square is an error.
(This dimensional analysis doesn’t care that $hat A$ is an operator and that it’s buried in the commutator. Units are great like that.)

Is there a Typo for the Generalized Uncertainty Principle in Griffiths Quantum Mechanics Fundamental Formulas?

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