Electron Pairs and Pauli

How can two electrons be in the same electron band, and act both under the electron cloud model and the Pallk Exclusion principle?
- Richard Ong (age 14)
Winston-Salem, NC, USA

The key here is that electrons have an internal property, not just a spatial wave form. The internal property is called spin. There are two independent spin states for an electron, so that allows there to be up to two electrons in the same spatial wave form without having more than one in the same quantum state.

Mike W.

(published on 12/17/2011)

Yes, but if we don't know their spin, then their spin can be anything as well, so their quantums numbers are the same, right?
- Richard Ong (age 14)
Winston-Salem, NC, US

The two electrons in the same wave state have opposite spins. If you express their spins in terms of values + or - on some axis, the spin state is (|+->-|-+>)/2^1/2. So in one sense they have the "same" spin state, in that either spin can point any direction, but they do know that they must always point opposite directions.

One of the weirdest things about quantum mechanics is that this property can be preserved even if the particles are separated in space. That's called "entanglement" or, as Einstein referred to it, "spooky correlations at a distance". Experimental violations of some conditions called the Bell Inequalities show that there really were no definite values for the spins themselves, even though there was a definite fact that the indefinite spins had to be opposite!

Mike W.

(published on 12/18/2011)