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I have a question regarding the interpretation of the relation $\Delta E \Delta t \ge 1$.

First, what is the exact meaning of $\Delta t$? We know that $\Delta E$ is calculated as the standard deviation of the energy distribution, but time is just a continuous parameter and there is no probability density associated with it. Can't measurements in non relativistic QM be done at precise time t?

Some undergrad texts explain this relation as "the longer you measure the energy, the less uncertain it is", but I feel this explanation is lacking. If we measure the energy of a particle, we should disturb it more, making $\Delta E$ larger!

Any input on this?

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  • $\begingroup$ I think you sort of answered your own question. The longer you measure, obviously the more uncertain its energy will become. Del(t) should denote the duration over which a given E is measured, and del(E) denotes the deviation in the measured E value. $\endgroup$
    – Lelouch
    Sep 15, 2016 at 17:56
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    $\begingroup$ Possible duplicate of What is $\Delta t$ in the time-energy uncertainty principle? $\endgroup$
    – John Rennie
    Sep 15, 2016 at 18:00
  • $\begingroup$ Hi Oti. See Josh's answer to the question I've linked above. $\endgroup$
    – John Rennie
    Sep 15, 2016 at 18:01
  • $\begingroup$ If we measure it for a longer time, then $\Delta t$ should be bigger, thus $\Delta E$ should be smaller, i.e. LESS uncertain. $\endgroup$
    – Oti
    Sep 15, 2016 at 18:21

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