Easy way to get the expectation value of momentum squared?

[chi-young]

Hello, I've been trying to define <p²> in terms of <x²>, much the same way that you can write <p> = m d<x>/dt, because it would be easier in my calculations.

Is this possible, or am I on a fools errand?

Edit: For Gaussian distributions.

 

[Simon Bridge]

To get p^2 you apply the position-space operator twice.
What's the problem?

Oh you want the classical relation - so you'd need the relationship between <p>^2 and <p^2>?