I got following expression regarding linear harmonic oscillator in quantum mechanics, and I don't understand what it means.
$[\langle(\Delta x)^2\rangle\langle(\Delta p)^2\rangle](t)$
$\Delta x$ and $\Delta p$ are the uncertainty of the position and the momentum, aka the Heisenberg's principle and they could be calculated as
$\Delta x = \langle(\Delta x)^2\rangle - \langle(\Delta x)\rangle^2$, where the angle brackets denotes the mean value and the result should be a number, right?
Then I dont understand why do I calculate $\langle(\Delta x)^2\rangle$, with the respect to time, because the expression is time-dependent.