## Schrödinger Equation

The Schrödinger equation describes how the quantum state of a physical system changes over time:

$$
i\hbar \frac{\partial}{\partial t} \Psi(\mathbf{r}, t) = \left( -\frac{\hbar^2}{2m} \nabla^2 + V(\mathbf{r}, t) \right) \Psi(\mathbf{r}, t)
$$
