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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.

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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.

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