This can't be right. The integral is between -a and a, and this would set <p^2> to 0. But <p> is 0, and that would make the variance 0, which would violate the uncertainty principle.
Thank you. I already found p, but my question is particularly about the part of the integrand that contains the partial derivative squared.
\frac{d^{2}}{dx^{2}}(a^{2}-x^{2}) dx
I don't know what to do with that.
Homework Statement
I am trying to find the variance of p for a wave function \Psi(x,0)=A(a^2-x^2)
I'm confused about how to set up the integral.
it should be something like -i^2h^2\int_{-a}^a A(a^2-x^2) (\frac{\partial\Psi}{\partial x})^2 dx
I'm confused about the partial...
Homework Statement
The book says to consider the gaussian distribution
p(x) = Ae-m(x-a)2
where A, m, and a are all positive, real constants.
I have no idea how to evaluate this! The book says to look up the relevant integrals. I see the integral of e-x2is pi1/2 but I don't know...