Electron Questions

EDBBOB · December 20, 2010

I'm 45 years old, and I went to school being taught, that the elementary particles were protons, neutrons and electrons. Recently I became aware of the Standard Model (what a mess), and it was like suddenly realizing that the earth wasn't flat, but it was actually a sphere...

I might be totally off with this question, but:

When you talk about the angular momentum of an electron (h-bar), is that to be considered as an actual spin of the particle along an axis, like a planet spinning along its poles?

Im quite new to Quantum mechanics, but:

Is it possible to express h-bar as radians/second?

If I understand correctly the electron is considered a point with no size / volume, but mass (and charge).

Does that give an electron infinite density?

Thanks for any answer

Best regards

EDBBOB

Erasmus00 · December 20, 2010

When you talk about the angular momentum of an electron (h-bar), is that to be considered as an actual spin of the particle along an axis, like a planet spinning along its poles?

Like many things in quantum mechanics, yes, but also no. First, electrons have a spin of 1/2, so an angular momentum along one axis of [imath] \frac{\hbar}{2}[/imath]. This seems pedantic, but its important. Spin 1/2 particle have a pauli exclusion principle, integer spin particles don't.

This angular momentum is analogous to a spinning top- whats different, and uniquely quantum mechanical, is that there is no defined axis. No matter what axis you measure you will find an angular momentum of [imath] \pm \frac{\hbar}{2} [/imath] The more you think about this, the more bizarre it will seem.

Is it possible to express h-bar as radians/second?

Its important to keep in mind that [imath] \hbar [/imath] is a measure of angular momentum, not spin. If you assume a momentum of inertia for an electron, you could derive a precession rate, however, quantum mechanically this isn't well defined.

If I understand correctly the electron is considered a point with no size / volume, but mass (and charge).

Does that give an electron infinite density?

Its more correct to say that there are no measurements that indicate the electron has size. But yes, this would give it an infinite classical density- specifically, a well understood form of distribution called a dirac delta function.