Standing Waves

No and no. <sees who it is> ohai.

You are thinking of deBroglie matter waves - in that model, then you can model electrons in a stationary state in terms of a dB standing wave. However, this model seems to have been pretty much discarded.

QM particles are not classical particles.
The "wave" performance is statistical in nature.
You know this.

There is a tendency to talk about the wavefunction and the particle being the same thing in wave-mechanics ... in this case the particle is "built up" from a superposition of stationary (basis) states. But one particle does not a wave make any more than cats exhibit wave-like properties.

 

I'm sure we've both been in discussions of "wave-particle duality" before.

That is pretty much what you are wrestling with here.

The way to think about it is this: fundamental particles are particles in the sense that when you catch (detect) one it arrives in one go rather than distributed over time. However, unlike classical particles, the statistics work a bit differently.

The similarity between the results of Quantum statistics averaged over many interactions and classical ray optics leads people to think there is some sort of wave motion thing happening and a lot of sloppy pop-science journalism ensues.

This paper:
http://arxiv.org/pdf/quant-ph/0703126]
by Marcella is rapidly turning into my goto for describing this - don't be intimidated by the math notation in there ... treat it as part of the jargon and read around it. The important point is that this is a pure QM treatment of quantum interference at slits with no wave optics type stuff at all. It also illustrates the formalism of wave mechanics - which is useful to get your head around when you are starting exploring this stuff.

The other good source are Feynman's lectures in QED that he did at Auckland Uni. You'll find them on YouTube. (Aside: they were shot in 8mm, transferred to VHS, and then to mp3 ... preserving them was touch and go.)

Depends on the situation - sometimes it is better to model a beam as a set of plane-wave states.

If I have a particle in a box length L and I've just measured it's position ... then I know x=μ to some classical uncertainty σ<<L ... so I can model the position of it's center of mass as being distributed as a gaussuan about a mean μ and varience σ². This function can modeled with a wave-function, which is a superposition of stationary-state wave-functions for a particle in a box.

The effect is. whatever energy state it was in before I made the measurement has been destroyed (by the process of measuring position) and it is now in a superposition of states.

IRL: the wavefunction (the real part anyway) for this sort of model will look like a sinusoid with a gaussian envelope ... you've seen pics like this before.