What is exactly Heisenberg’s uncertainty principle?

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According to Classical mechanics, a moving particle at any instant has fixed position in space and definite momentum which can be determined simultaneously with any desired accuracy. This assumption is true for objects of appreciable size, but fails in particles of atomic dimensions.

 

·         Since a moving atomic particle has to be regarded as a de-Broglie wave group, there is a limit to measure particle properties.

·         If the group is considered to be narrow, it is easier to locate its position, but the uncertainty in calculating its velocity and momentum increases.

·         If the group is wide, its momentum is estimated easily, but there is great uncertainty about the exact location of the particle.

 

Heisenberg a German scientist in 1927, gave uncertainty principle which states that “The determination of exact position and momentum of a moving particle simultaneously is impossible’’.

In general, if △x represents the error in measurement of position of particle along x-axis, and △p represents error in measurement of momentum, then

                                                                              △x. △p = h

Or limitation to find the position and momentum of a particle is

                                                                           (△x).(△p) ≥ h/4π

i.e. Heisenberg uncertainty principle states that both the position and momentum  cannot be measured simultaneously with perfect accuracy.

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