8/22/11 - 9/9/11 The Quantum World Spectroscopy: photons

### 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.