By solving Schrodinger equation $H\psi = E\psi$ using Green function I get
$$\psi(x) = \int G(x,x')E\psi(x') dx' $$
by taking abs of $\psi$
$$|\psi(x)| \leq E \int |G(x,x')\psi(x')|dx' \leq E \sup_{x'}(\psi(x')) \int |G(x,x')|dx' $$
Why is it possible to take out $\psi$ from the integral with $\sup$?
And what does it mean
$$\frac{|\psi(x)|}{\sup_{x'}(\psi(x'))} = |\psi(x)|_\infty$$
Thanks for help! :)