Schrodinger’s Function
Def.$$i\hbar\frac{\partial}{\partial t}|\Psi(t)\rangle=\hat{H}|\Psi(t)\rangle$$
If we consider a steady-state result, we have
$$i\hbar\frac{\partial}{\partial t}|\Psi(t)|=\hat{H}|\Psi(t)\rangle\Rightarrow\frac{-\hbar^{2}}{2m}\nabla^{2}\Psi(\vec{r})+V(r)\Psi(\vec{r})=E~\Psi(\vec{r})$$ where V(r) is the potential and E is the energy of the object(s).