# Dirac on Spreading Wave Packets

1. Aug 4, 2014

### Staff: Mentor

My layman's intuition tells me that wave packets normally spread out in space and disperse, except in special circumstances. Photons don't behave like that.

In The Principles of Quantum Mechanics, pp 124-125, Dirac discusses the equations of motions of a photon wave packet. He says:

Thus Dirac doesn't show that the packets don't disperse, he imposes it as a condition on the solution. I presume that the thing he left unsaid was "because that agrees with experiment," which is a compelling argument.

However, on the very next page he seems to waffle:

"the wave packet undergoing a spreading" So what's the deal? Photon wave packets do or do not spread?

2. Aug 4, 2014

### Avodyne

For a photon in free space, the wave packet does not spread. This is a consequence of the dispersion relation for a massless particle, $\omega = ck$, where $\omega$ is the angular frequency and $k$ is the magnitude of the wave number. This is also true in classical EM: wave packets propagate without changing shape.

See http://en.wikipedia.org/wiki/Dispersion_relation

3. Aug 4, 2014

### Jilang

Sure they do, they spread out lots. Think of diffraction.

4. Aug 4, 2014

### The_Duck

Right.

For photons, the associated wave packet represents something like the *probability* to find the photon at a given position. This wave packet of probability does spread out. But the photon is only ever detected at a single position.

It sounds like Dirac is setting up initial conditions at t=0. He is not claiming that the wave packet doesn't disperse as you let time run forward. Indeed, in the next quote you give he discusses the fact that the wave packet spreads out as t increases.

5. Aug 4, 2014