How to prove Δx and Δp obey the Heisenberg uncertainty principle?, chemistry homework help

How to prove Δx and Δp obey the Heisenberg uncertainty principle?, chemistry homework help

The spread in an observable is ΔA =(A^2 – (a)^2)^1/2 where A is the expectation value for the operator A hat.

How do I evaluate knowing this Δx and Δp for the particle in a box to show it obeys Heisenbergs uncertainty principle?

Also, why is the expectation value P^2 not equal to p^2 and the same for the expectation value of X^2 not equal to x^2?

 
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