I have an expression like this:
$$U(x,p)=e^{-ix(p^2/(2k))}\cdot e^{ix(k(m^2-1)/2)}$$
with
$$U(x,p)=\int_{-\infty}^{\infty}u(x,z)e^{-ipz}dz$$
How do I find $u(x,z)$ I am not sure how to approach this at all?
The first thing to do I think is to make the two statements equal: $$\int_{-\infty}^{\infty}u(x,z)e^{-ipz}dz=e^{-ix(p^2/(2k))}\cdot e^{ix(k(m^2-1)/2)}$$
But now I don't know what to do. Thanks for help.
Hint:
$$u(x,z) = \int_{-\infty}^{\infty}U(x,2\pi q)e^{2\pi i q z} dq$$
Note:
Typically $$F(\omega; \cdot) = \int_{-\infty}^{\infty}f(t; \cdot)e^{- 2\pi i \omega t} dt $$ and $$f(t; \cdot) = \int_{-\infty}^{\infty}F(\omega; \cdot)e^{2\pi i \omega t} d\omega $$
So I rewrite your $p$ as $p=2\pi q$