Understand Uncertainty Principle in a Week

[pmb_phy]

It appears that another common misconception is the definition of the uncertainty of an observable. By definition the uncertainty in the physical observable A is given by

$\Delta A =\sqrt{\langle(A-\langle A\rangle)^2\rangle}$

In case someone wishes to know where this comes from I scanned and uploaded the defintion from Quantum Mechanics, Cohen-Tannoudji et al. The two pages are at

http://www.geocities.com/physics_world/uncertainty_01.jpg
http://www.geocities.com/physics_world/uncertainty_02.jpg

This same definition appears in ever single text that I've ever read in which $\Delta X$ is explicitly defined. It is evident from those pages that the Heisenberg Uncertainty Principle is really a misnomer since a principle is something which, by definition, cannot be derived from more elementary postulates. However the uncertainty relation is a derivable relationship.

Pete