questions on wave particles

[Baby Astronaut]

If a wave is observed, I'm thinking it becomes a particle. It collapses into that shape, at least. If correct so far, then shouldn't it lose its wave/particle duality after the collapse, and just be a particle?

 

Taking it further (...if such is the case that it becomes a particle only), does it ever revert back to its wave/particle form?

 

Also, something from another thread...

Not really, the interaction results in a momentum change for the electron, all interactions do. This results in no interference.

What is the difference between observing an electron and a photon randomly bumping it? Why doesn't it act the same as purposeful interaction/observation?

[ajb]

If a wave is observed, I'm thinking it becomes a particle.

 

A classical particle is considered to be a point-like object. Now, quantum mechanics tells us that this is not really a good way to view things.

 

What is not stressed enough in standard presentations of quantum mechanics (via Schroedinger or Heisenberg) is that we have in reality a classical field theory. The notion of a particle gets replaced by a field over space, this is the wave function. We pass from a point-like description to an extended wave-like one. In a sense, the particle becomes speared into a little fuzzy blob.

 

The closest thing to a "particle" in this description is a highly localised wave-function.

 

What I think you are confusing is the notion of wave-function collapse.

 

What this says (roughly) is that all possible states are combined linearly into the actual state the particle assumes. Up on measurement one of these states is selected. (Like spin up or down or whatever.)

[Baby Astronaut]

We pass from a point-like description to an extended wave-like one. In a sense, the particle becomes speared into a little fuzzy blob.

What is the diameter of such an extended wave? Greater than an orange/apple?

 

The closest thing to a "particle" in this description is a highly localised wave-function.

That's the reason for the question above. How localized is the wave? I had thought it extended to infinity.

 

What I think you are confusing is the notion of wave-function collapse.

 

What this says (roughly) is that all possible states are combined linearly into the actual state the particle assumes. Up on measurement one of these states is selected. (Like spin up or down or whatever.)

I'm probably confusing it because of the double-slit experiment. If the wave becomes like a particle after it's observed, this doesn't seem to have anything to do with spin up or down (or "whatever" ).

[ajb]

Generically you are right, the wave extends to infinity. However, often most of the wave will be concentrated somewhere. This is the most likely place to find the particle.

 

For a free particle, the wave is a plane wave. In essence it could be anywhere! (Technically plane waves are not [math]L^{2}[/math], so you have to extend the Hilbert space to include them)

 

Localised states comprise of a superposition of plane waves with "spatially concentrated extent". This is a "wave packet". A typical example could be the Gaussian wave packet.

 

You have to take into account the uncertainty principle. So the more concentrated in space the wave packet is, the more the momentum is spread out.

[Mukilab]

So if you took the question 'how long is a piece of string'.

 

You might SAY it's 100mm or whatever but in fact it's infinite as you can ever get smaller and more localized, emphasized by the wave-like fuzziness of the field?