How does an electron move around in an orbital? Is it "wave-like" or random?

When an electron is moving around in its orbital, is it actually moving around like a wave, like this video shows? (By wave-like, I mean, the 'electron' in this video is showing it following a predictable wave-like path, which would mean you could precisely determine its position which obviously you can't). Or, instead, does it just have some probability to be in that orbital's space, and just randomly jumps around from one point to another? Or if not that, how does the electron move around in its orbital?

Orbitals are solutions to time-independent quantum wave equations.

That is, there is no time-dependence. There is no little ball in there moving around, the electron has a quantum characteristic and exists with neither a well defined position nor a well defined momentum.

• However, it does have a well defined angular momentum, just to make things confusing. Sep 14 '14 at 21:41
• Worth repeating: There is no little ball in there moving around. Sep 14 '14 at 23:49
• Confusingly enough, you can however take a picture of the little ball in there, with a definite position. Even though there is not little ball moving around... However, when you do that, the little ball is no longer "in" the orbital.
– Aron
Sep 15 '14 at 3:25

dmckee is right. However I would like to add some notes to provide an intuitive connection between the asker's question and the answer.

When we conceive of the orbital as a 2-dimensional surface in 3-dimensional space, as in the video above, we are not looking at the orbital. We might be tempted to say we are looking at the outline of the orbital, but the orbital extends infinitely into space. What we are actually looking at is a surface, within which the probability for the electron to be found is less than some number, for example 90%. Generally, a different choice of probability will not change the shape of the surface. This is convenient for the purpose of understanding what orbitals look like.

That being said, the orbital is not a 2-dimensional surface in 3-dimensional space. The orbital is a complex scalar in 3-dimensional space, meaning that for every point $(x,y,z)$ the orbital has a real and imaginary part. That being said, we generally only care about the magnitude which is a positive real number. The physical meaning of this number is the probability per unit volume, for the electron to be found at this point in space.

• FYI, calculating the surface within which there is 90% probability is actually quite challenging unless the orbital is really simple and analytic. So usually what is plotted is just an isosurface on which the probability density is at a given figure, because that's much easier. Sep 15 '14 at 13:16
• Isosurface, that's the word i was looking for. Thank you Sep 15 '14 at 16:49

Neither. Electrons in "orbitals" are not moving (I don't like the term "orbital". I leave it to chemists. I prefer "wave function". More exactly, wave function of a stationary state. This means that nothing changes in time.)

It isn't even correct to identify a wave function with a "probability amplitude", i.e. as giving probability density with its modulus squared. It is true, but it isn't all. A wave function allows you to compute the mean value of any observable you want, e.g. angular momentum. As @JerrySchirmer notes, an electron in a stationary state may well have a definite (non-zero) angular momentum (not necessarily, however).

The electron does not have a definite position, neither can you say it is moving ... and so on. If all this sounds paradoxical, welcome to quantum mechanics. One point is never too much emphasized: you cannot understand QM concepts by reducing them to classical world. Entirely new ideas are at work there, and current language has no hope to express them, not even approximately.