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The Uncertainty Principle for Energy and Time 

The Uncertainty Principle says that the product of the unceratinty Δx of the location of a particle and the
uncertainty of the momentum Δp_{x} can be no smaller than ½h, where h
is Planck's constant divided by 2π; i.e.,
It is also true that the product of the uncertainty in the energy ΔE of a particle and the uncertainty concering time Δt must
be no smaller than ½h. Thus
The energy E of a particle with mass m and velocity v is ½mv². Its momentum p is mv. Therefore the energy expressed in terms of momentum is
The change in energy δE resulting from a change δp in momentum is given approximately by
Thus the uncertainty ΔE in energy is given by
The uncertainty in time Δt is given by
Thus
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