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But by the definition of this uncertainty principle :

##E\,\Delta t \geq \dfrac{\hbar}{2}##, I can write :

##\Delta t \geq \dfrac{\hbar}{2E}##, then ##\Delta t## has a lower limit and not an upper limit.

If this was a upper limit, this would mean that ##\Delta t##, i.e. the apparition time, should be observed in a time interval lower than ##\dfrac{\hbar}{2E}## : for example, if a detector had a time resolution greater than ##\dfrac{\hbar}{2E}##, the particle could not be detected, could it ?

So in which case can we write : ##\Delta t \leq \dfrac{\hbar}{2E}## ??

It seems that I have confusions with this principle.

Any clarification is welcome