Welcome to the beginnings.

I’m just testing some mathematical symbols.
Schrödinger’s Equation (time-dependent):
\[-i \hbar \frac{\partial}{\partial t} \Psi = \hat{H} \Psi\]
That is equivalent to:
\[-i \hbar \frac{\partial}{\partial t} \Psi(\vec{r},t) = \bigg[\frac{-\hbar^2}{2m} \nabla^2 + V(x) \bigg]\Psi(\vec{r},t)\]

For time-independence (and we have an eigenvalue problem):
\[\bigg[\frac{-\hbar^2}{2m} \nabla^2 + V(x)\bigg]\psi(x) = E \psi(x)\]