What is the Correct Formula for Uncertainty of a Particle?

[kasse]

$$\Delta E = \sqrt{(E - <E>)^{2}}$$

This is evident. However, I don't understand why

$$(E - <E>)^{2}$$ can be written $$E^{2} - <E>^{2}$$

 

[Dick]

I think what you mean is < (E-<E>)^2 >=<E^2>-<E>^2. <(E-<E>)^2>=<E^2-2E<E>+<E>^2>=<E^2>-2<E><E>+<E>^2. Right?

 

[borgwal]

$$\Delta E = \sqrt{(E - <E>)^{2}}$$

This is evident.

I'll say it once more: you have to read your textbook: you might think this is evident, but actually it's wrong. What your textbook will say is that

$$\Delta E = \sqrt{<(E - <E>)^{2}>}$$