# Can photon form wavepackets?

1. Sep 7, 2004

### touqra

Can photon form wavepackets? I mean we can't detect the location of a photon right? So this means delta x is infinity, which implies that photon is a plane wave, which is not a wavepacket?

2. Sep 7, 2004

### humanino

Not exactly. You can detect a single photon, with the usual rules for the accuracy in position and momentum. You can actually see a single spot on a screen for instance, if the luminosity of the source is very small. The actual size of the spot is of-course non-zero. It is also true that, before you detect it, the photon with a well defined wavelegth is a plane wave. Depending on how it has been created, the indeterminacy in wavelength can be more or less large. Laser photons have a vanishingly small wavelegth undeterminacy.

A plane wave is a trivial wavepacket.

3. Sep 7, 2004

### Fredrik

Staff Emeritus
Suppose a photon is emitted from a light source inside a box with walls that won't let photons through. This photon obviously doesn't have delta-x equal to infinity.

The answers to your questions are: Yes, photon states can be "wave packets", and no, they aren't always plane waves (=momentum eigenstates).

4. Sep 7, 2004

### touqra

When will they be plane waves? And when will they be wave packets, beside the situation where you mentioned?

I agree with your explanations but I have a question. As in for other particles like electron, that we can detect exactly its position, can we detect a photon's location with 100% accuracy compromising our knowledge on its wavelength? If we can detect it 100% accurate, does this violate the speed of light limit of relativity?
A detector uses electromagnetic wave in some way for any detections. How could you detect a photon with a photon?

Last edited: Sep 7, 2004
5. Sep 8, 2004

### Fredrik

Staff Emeritus
A plane wave is a momentum eigenstate. A wave packet is a superposition of momentum eigenstates. The state of the photon is never exactly a momentum eigenstate, so I suppose you can say it's always a wave packet, or at least that it's never a plane wave. (Its momentum-space wave function can be "sharp", but never quite as sharp as the Dirac delta function).

I don't think we can detect anything with 100% accuracy. When it comes to measuring positions, the best we can do is to determine a region of space where the particle is. After the measurement, the wave function will be 0 outside that region.

I don't see why accurate measurements would violate the relativistic speed limit.

You wouldn't detect photons with photons. You would have the photon knock an electron loose from the surface it hits, and amplify the signal until you get a measureable current. This is roughly how a photomultiplier works.