Euler’s formula relates the complex exponential function to the trigonometric functions.
\[e^{i\theta}=\cos(\theta)+i\sin(\theta)\]
The Euler-Lagrange differential equation is the fundamental equation of calculus of variations.
\[\frac{\mathrm{d}}{\mathrm{d}t} \left ( \frac{\partial L}{\partial \dot{q}} \right ) = \frac{\partial L}{\partial q}\]
The Schrödinger equation describes how the quantum state of a quantum system changes with time.
\[i\hbar\frac{\partial}{\partial t} \Psi(\mathbf{r},t) = \left [ \frac{-\hbar^2}{2\mu}\nabla^2 + V(\mathbf{r},t)\right ] \Psi(\mathbf{r},t)\]