snatchingthepi said:
I think most people use Griffiths book because it is "simple" and "conversational" and doesn't put too much work into prerequisites. I found this a bloody disaster and my confusion was immediately cleared-up when I switched to Zettili.
I had a quick look at Zettili. Very interesting.
"Energy and time, for instance, form a pair of complementary variables. Their simultaneous
measurement must obey the time–energy uncertainty relation:
$$\Delta E \Delta t \ge \frac{\hbar}{2}$$
This relation states that if we make two measurements of the energy of a system and if these
measurements are separated by a time interval ##\Delta t## the measured energies will differ by an
amount ##\Delta E## which can in no way be smaller than ##\frac{\hbar}{\Delta t}##."
Griffiths has too much to say on the time-energy relation to quote it all, but regarding the HUP he says:
"The position-momentum uncertainty principle is often written in the form:
$$\Delta x \Delta p \ge \frac{\hbar}{2}$$
##\Delta x## (the uncertainty in ##x##) is loose notation (and sloppy language) for the standard deviation of the results of repeated experiments on identically prepared systems."
I prefer Griffiths' precision, even though his book has a reputation for being simplistic. Unlike Zettili, when he dodges an issue, he always let's you know.
