i have this equation :
$$-\varepsilon^2\Delta u+V(x) u= h(x) f(u)$$ can i consider it as a Schrodinger equation:
$$ i\varepsilon \frac{\partial \Psi}{\partial t}=-\varepsilon^2\Delta \Psi+(V(x)+E)\Psi-|\Psi|^{q-2}\Psi,~x\in \mathbb{R}^N$$ $$\Psi(t,x)=\exp(\frac{-iET}{\varepsilon})u(x), ~u:\mathbb{R}^N\to[0,+\infty)$$
What is $h(x) f(u)$ in this case please ? ($h,f:\mathbb{R}\to \mathbb{R}$ continuous )