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• Spin In this video, we're going to start looking

• at something called Spin. Spin was something that was only discovered when people started

• experimenting on very small things like electrons. I'm going to tell you about some of the experimental

• facts that they found.

• Firstly, what is it? We know that normal objects can have all kinds

• of measureable properties like Position,

• Speed, Temperature

• etc

• Spin is another one of these properties that you can measure of a particle. And in the

• same way that a particle can have different positions and can change it's position, the

• spin of an object can take different values and change over time.

• But unlike those other properties, it's hard to describe what it actually is intuitively.

• The best I can do is say that the spin of an particle measures how magnetic it is, and

• decides which direction the magnetic field is pointing. The problem with this statement

• is that it makes particles seem like they act like tiny little bar magnets. Actually

• they don't, because as we'll see, spin is a very strange thing.

• From here on in we're going look at the spin of electrons. Whenever we measure spin, we

• have to pick a direction, aka an axis, to measure it in. Let's call the direction pointing

• east the x axis, and the direction pointing north the y axis. Then say I happen to know

• that an electron has spin of some strength that I'll call s, in the x direction. It's

• tempting to say the electron is like a bar magnet pointing in the x direction. But if

• that was the case, how much spin would you expect the electron to have in the y direction?

• Well the y direction is perpendicular to x, so you normally we wouldn't expect there to

• be any magnetic field that way at all. However if you measure the spin in the y direction

• you will get a very weird result. Say we do this experiment record the results, then do

• it again using a new electron and keep repeating. Half the time you will find that the particle

• not only does have spin in that direction, its strength is still s. The other half of

• the time? It will still have strength s but this time in the negative direction of y!

• This is completely unexpected. But notice something. If we take the average of the results,

• we get 0, which was the result we thought we'd get. Hm, let's try another example

• Let's say we have a particle with spin s in the x direction again. We'll pick the 45 degree

• axis to measure spin in. What would we normally expect? Well the 45 degree angle axis is still

• somewhat pointing in the x direction, so we'd expect there to be some spin in that direction

• but a smaller amount than s. We can calculate how strong we think it would be using vectors

• and get that the new spin should be s on root 2. But what happens when I measure it? Again,

• every single time I repeat this experiment, the electron will have spin of strength s,

• but this time, it will be slightly more likely to be in the positive direction than the negative,

• so that when I take the average of all my results I get s on root 2. Again, though each

• individual trial was unexpected, the average result is what I thought I'd get.

• Let me summarize the two things we can learn about the spin of an electron from these kinds

• of experiments Firstly, no matter what direction we measure

• the spin in, its value will always be positive s or negative s where s is equal to this number.

• We'll give these two possibilities some convenient names: up and down. So you can for example

• say that an electron is spin down in the y direction.

• The second weird thing is that, where ever you'd normally expect an electron to have

• a certain spin in a direction, let's say spin equal to k, you will instead find that each

• time you measure you only get spin up or down but when you average the spin of each trial

• you get the right result, Ie averaging your data will give you k.

• So you see, its possible to say which direction an electrons spin is in and its strength but

• it's not really like the classical situation with a bar magnet. With a bar magnet, knowing

• how strong the magnet is, and in what direction, allows you to find its strength in every other

• direction. That's not the case with spin. When there's lots of particles, on average

• they act just like bar magnets, but individually they act like they're equally strong in all

• directions they're measured in and act randomly. We still don't know if that randomness is

• true randomness though, and we still don't know what spin really is.

Spin In this video, we're going to start looking

B1 中級

スピン (Spin)

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Cheng-Hong Liu に公開 2021 年 01 月 14 日