It is known that gaussian wave packet happen to be minimum uncertainly wave packets. In this case, if the uncertainty of coordinates Δx and the uncertainty of wave number Δk are taken as the standard deviations then this minimum value is
In this way, we can write
Δx is the uncertainty of coordinates, Δk is the uncertainty of wave number
The wave number is equal to
where h is the Planck constant, p is the momentum
Using (2) we have
Where Δp is the uncertainty of momentum
We put (3) in (1)
where
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