Question

finding the normalization constant question

Answer 1

would I just set this equal to 1 and take the integral?

Answer 2

It's a PDF (?), so yes.

Using M.Wolfram for the integration, looks like: \(N = \left( \dfrac{\beta m}{2 \pi} \right)^{\frac{3}{2}}\) ... for \(Re(\beta m) > 0\).