Question

what is Heisenberg uncertainty principal?Derive it on the basis of wave packet?​

Answer 1

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Principle:

Heisenberg's uncertainty principle states that it is impossible to measure or calculate exactly, both the position and the momentum of an object. This principle is based on the wave-particle duality of matter.

Derivation:

A quantum mechanical system is characterized by a complex function defined over space called its wave function. The wave function is such that its squared magnitude is equal to the probability density for the system. That is to say, if ψ(X) is the wave function value for a particle at the point X then the probability density at X is |ψ(X)|²=ψ(X)ψ(X), where ψ(X) is the complex conjugate of ψ(x).

For a system with a wave function ψ(X) the expected value of a variable f(X) for the system is given by

⇒E(f(X)) = ∫f(X)|ψ(X)|²dX

             = ∫ψ(X)f(X)ψ(X)dX

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