TITLE: Calculating expectations values from density matrix in position basis
QUESTION [0 upvotes]: given I know the density matrix elements in position basis as a function of time.
$ \langle x | \rho(t) |x' \rangle$
How do I calculate the expection values like $\langle x^2(t)  \rangle $ or $ \langle p^2(t) \rangle$ from this?

REPLY [1 votes]: I think I got it myself:
$\rho = \int dx dx' \langle x |\rho| x' \rangle |x \rangle \langle x' |$
Then it follows:
$\langle x^2 \rangle = \int dx \langle x |\rho| x \rangle x^2$,
right?
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