Question

Prove heisenberg's uncertainity principle.

Answer 1

$\sf{\underline {Heisenberg's\: Uncertainty\:Principle}}$ :

It states that " it is not possible to measure simultaneously both the position and momentum of a microscopic particle, with absolute accuracy.

Δx × Δp ≥ $\frac{h} {4π}$

Δx = Uncertainty in position

Δp = Uncertainty in momentum

h = Planck's Constant ( 6.626 × 10^ - 34 Js )

If the position of a particle is measured accurately, there will be more error in the measurement of Momentum. Conversely, if momentum is measured accurately , the position will not be accurately known.

Since, p = mv ( mass × velocity )

So, Δp = mΔv because mass is constant.

Δx × mΔv ≥ $\frac{h} {4π}$

Δx × Δv ≥ $\frac{h} {4πm}$

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Answer 2

Actually your question has no answer !

It should be => Write the Heisenberg's Uncertainty Principle.

ANSWER

Actually this is just a principle given by him and it doesn't have any such proof or we can say that we can't prove it in simple words.

Reason

Because when something is proven in mathematics correctly then it doesn't change.

Heisenberg`s Uncertainty Principle

1)HUP states that it is impossible to determine continuously and simultaneously the exact and correct position and velocity of an particle at the same time.

2)But not all object follow this principle in quantum world also.

Like we can take the example of Photon (a massless particle) which is component of light rays and normal Heinsenberg uncertainty principle doesn't apply to it as they cant be localised untill destroyed.

3)The Equation of HUP is in attachment.

4)It is Helpy to determine the nature if fundamental particles of nature.

-But some says that this principle applies to the particles in quantum world only but I am not clear yet and the quantum world itself is very mysterious.

-In quantum world anything(I mean which can't be imagined in real world) could happen anytime without any reason !This might sound weird but its true.