I'm trying to understand the concept of uncertainty in relation to derivatives for a large quantum system, i.e. one with many degrees of freedom.(adsbygoogle = window.adsbygoogle || []).push({});

When is it true that σE/σt ~ dE/dt? ---- 'σ' is the uncertainty

First, I know there is no time operator in quantum mechanics. I'm not sure how to work around that, perhaps we could try the question with momentum and position. The point is, for a large quantum system, can I approximate the rate of change of energy with the uncertainty of energy divided by the uncertainty of its age?

I've tried unconventional methods to answer the question. First using an assumption that:

i/ħ d^{2}/dt^{2}ψ = dE/dt ψ

then trying to compare it to the uncertainty calculation assumed as follows:

(σE)^{2}= (∫ ψ*Eψ dt)^{2}- ∫ ψ* E^{2}ψ dt

Which gives equal results for a Gaussian wave function. But I'm not sure how to go about this question in a more conventional way.

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# I Question for large quantum system

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