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#### 4.6 Heisenberg uncertainty principle

Heisenberg proposed the uncertainty principle in connection with the dual nature of waves and particles. The uncertainty principle has been explained in the following way: suppose if a particle is moving along X–direction, then according to uncertainty principle, it is impossible to measure accurately simultaneously its position (x) and also its momentum (px). If Δx is the uncertainty in measuring its position then Δpx is the uncertainty in measuring its momentum.

Then,

ΔxΔpxh _____ (4.51)

where h is Planck’s constant

The above equation is applicable in all directions. Along Y– and Z– directions, it is:

ΔyΔpyh     and     ΔzΔpzh _____ (4.52)

The above uncertainty has been already proved using ...

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