Direction of a single particle wave

[Gerinski]

Amateur level.

Popular Science books usually start describing the double-slit experiment in terms of waves, by showing a drawing in which waves are pictured as concentrical circles emerging from the source. When passing through the slits, new concentrical circles are drawn emerging from each slit.
When the circles reach the screen it's easy to understand the building up of interference.

Then they go on saying that you may tune the source beam so that it emits a single particle (eg an electron) at a time. This gives me a problem for understanding the wave picture.

A concentrical circle expands from the source point or slit towards every direction (the circle is a 2-dimension drawing but obviously it represents concentrical spheres).
But when we consider a single particle, obviously it can not travel to any and every direction.

When we think of the beam firing a single particle at a time, and we want to use the wave picture, can we think of it as a spherical wave expanding in all directions? this would seem weird!
Or do we have to think of it as an ondulation traveling along a single line direction as we do when we use the point-particle picture?

But if we think of the wave as an ondulation along a single line, it becomes difficult to see how interference would build up, doesn't it?

Thanks!

 

[Gerinski]

Sorry, as nobody posted any reply in 4 days, I wonder if my question was too stupid to deserve any.
Even if the answer is that the question is worthless I would appreciate someone to tell me.

Maybe to clarify a bit, when I say "thinking of a wave as an ondulation traveling along a single line", I do not mean actually "a single straight line", otherwise it would be no big difference with the particle picture.

What I imagine is more something like "a wave traveling towards a definite direction, which would be "strongest" along that direction line path, and as the angle gets bigger away from the direction path, the wave gets dimmer and dimmer."

 

[seratend]

A concentrical circle expands from the source point or slit towards every direction (the circle is a 2-dimension drawing but obviously it represents concentrical spheres).
But when we consider a single particle, obviously it can not travel to any and every direction.

You have to view, in this case, the wave as the probability density location of the particle. Hence a single particle may have a non nul probability density in a given area of the space but it may only be located on a given location.

Seratend.

 

[Q_Goest]

When we think of the beam firing a single particle at a time, and we want to use the wave picture, can we think of it as a spherical wave expanding in all directions? this would seem weird!
Or do we have to think of it as an ondulation traveling along a single line direction as we do when we use the point-particle picture?

From the perspective of another amateur (ie: I don't know the math of QM) I believe a photon can be thought of as being emitted in a random direction as the electron moves from one energy state to another, with the photon having an energy equal to the energy given up by the electron. So you would be correct to consider it a spherical wave expanding in all directions. However, once it's created, it can be manipulated into a beam.

 

[CarlB]

When we think of the beam firing a single particle at a time, and we want to use the wave picture, can we think of it as a spherical wave expanding in all directions? this would seem weird!

Yes, you can use the spherical wave picture for a single electron. We all think it's weird too.

Or do we have to think of it as an ondulation traveling along a single line direction as we do when we use the point-particle picture?

No, we can't think of it this way. The experimental evidence is pretty clear in indicating that even single electrons interefere with themselves. In order to interfere with themselves (and produce those interference patterns), the electron must travel in more than one direction on emission.

Now that you've lost your virginity as far as the electron going in two directions at once, you might as well go the rest of the way and assume that the electron travels in all directions at the same time. Thus the spherical waves that you saw in the Popular Science article.

Carl