What is your favorite equation?

[zeromodz]

It can be about anything. I am kind of new to physics and I love playing with new interesting equations like time dilation and so forth. Whats your favorite equation that you use to calculate things for fun?

 

[Phrak]

electromagnetism: d(*+i)dA = -*J

 

[msbell1]

Lagrange's equations

$$\frac{d}{dt}\frac{\partial L}{\partial\dot{q}} -\frac{\partial L}{\partial q}=0$$

 

[dE_logics]

The set of equations as in the attached PDF.

 

[Hootenanny]

Am I allowed two interrelated equations? If so, I'll have Maxwell's equations

$$F_{\left[\alpha\beta,\gamma\right]} = 0$$

$${F^{\alpha\beta}}_{;\beta} = \mu_0J^\alpha$$

 

[ApexOfDE]

Maxwell eqs.

 

[intervoxel]

The symmetrization requirement in QM:

$$\psi(\textbf{r}_1,\textbf{r}_2) = \pm \psi(\textbf{r}_2,\textbf{r}_1)$$ (+for bosons, - for fermions)