Physics — The Schrödinger Equation

i\hbar\frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat{H}\Psi(\mathbf{r},t)

\hat{H} = -\frac{\hbar^2}{2m}\nabla^2 + V(\mathbf{r})

-\frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2} + V\psi = E\psi

E_n = \frac{n^2\pi^2\hbar^2}{2mL^2}