# What does it mean: $[\langle(\Delta x)^2\rangle\langle(\Delta p)^2\rangle](t)$?

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.

For an observable $$O$$, we define $$\langle O \rangle (t) = \langle \psi(t) | O | \psi(t) \rangle$$, where $$| \psi(t)\rangle$$ is the state of the system. The time dependence of the expectation comes from the time dependence of the state.