大学物理-量子物理 (5)

Transcript

05-5 Exclusion

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501 Avatar5-Exclusion

CHAUCER: Now it’s time to investigate one of the most important properties of elementary particles… one that literally shapes the atoms of each element in the periodic table. Jeeves, please continue.

505 Exclusion

JEEVES:

We have just discussed how Schrödinger’s Equation shows us how to accurately describe fundamental particles with a “Wave Function”, now, let’s examine why two electrons together reveal a feature of quantum mechanics totally unlike anything in the large-scale world we inhabit.

In a classical setting, even if two things are identical, they are still individuals. As long as we keep track of them carefully, we can treat them separately and label them A and B… or X and Y… or 1 and 2.

But consider what is different about a two-electron system – whether in an atom or in a box it doesn’t matter. Since the two electrons are constantly phasing in and out of existence and since they are absolutely identical, it is impossible to keep track of a specific individual. Because of this we must use a combined wave function to describe the pair rather than use two individual wave functions.

This new two-particle wave function will have two parts to it. And those parts will either add or subtract. Physicists would say this makes the wave function either symmetric or anti-symmetric.

And it turns out that only the anti-symmetric function works for electrons. (and quarks and protons and neutrons).

Let’s let this red wave represent the first part of the combined wave function and this green wave represents the negative of the second part. If the electrons are in the same state, these two waves will be mirror images of one another.

AS one goes up, the other goes down in perfect synchrony.

So, when we combine them, we get no wave at all. And since the wave is a map of the electrons existing at that point, no wave means no electrons!

So clearly, two electrons can never be in the same state because that causes their combined wave function to disappear.

Now the only components making up the “dynamical state” in the atom is the shell it occupies and another property that electrons have – called “spin.” You can think of electrons as little spinning tops if that helps. And these electron-tops can spin in only two ways -- upright or upside down, which can make them distinguishable.

So the end result is that 2 and only 2 electrons can occupy each shell in an atom….one with spin up and the other with spin down. Other electrons in the atom must occupy higher and higher shells.

This is called the “Pauli Exclusion Principle” first espoused by Wolfgang Pauli.

Without this exclusion, all electrons would occupy the lowest energy state and atoms would behave VERY differently and the universe would be a VERY different place!

510 Bosons and Fermions

The fact is that the property called “spin” is quantized as well (no big surprise). And all particles fall into one of two different families because of this.

Those particles that have spin equal to ½ or 3/2 or 5/2 and so on form the family of fermions. The name comes from Enrico Fermi who along with Paul Dirac developed the statistical methods for dealing with them. Fermions are said to have half-integral spin. And as indicated above, electrons, quarks, protons, neutrons are in this family.