Albert Einstein's equation relating mass and energy
E² = m²c⁴ + p²c²
The equation is so often turned into E=mc² because for a massed particle, the momentum is so small that the p²c² term is negligible.
Photons and the Pauli exclusion principle
Photons do not obey the Pauli exclusion principle; they are gregarious particles.
Energy for a free particle
Energy = mass-energy + kinetic energy.
For a non-free particle, add the potential energy (i.e. the p²c² term).
p = h / λ
A Fourier principle that holds as a special case for freely moving particles such as photons or electrons not stuck in a box; hence, the wavelength of the particle replaces the length of the box.
Waves and quantum particles
The Heisenberg priciple, with its Fourier-conjugate relationship between momentum and distance, imparts on quantum particles properties usually reserved for waves.