Spin in Quantum Mechanics: What Is It and Why Are Electrons Spin 1/2? Physics Basics

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Hey everyone, I'm back with a new video! In this episode of "Quantum Mechanics, But Quickly", we're looking at the basics of Spin!

Spin is a very interesting topic that is not studied in detail until you choose to undertake a degree in physics. And yet, spin is commonly described at high school or even earlier, and we're often just told to accept that it exists. Instead of accepting it, I thought we'd take a look at what spin actually is.

Scientists noticed that some particles behaved as if they had angular momentum. For those of you familiar with angular momentum, it's just like linear momentum (p = mv), except an object gains angular momentum when it moves along an angular path (e.g. orbiting around a planet, spinning like a top, etc.).

The trouble was, the particles that seemed to have this angular momentum were showing no evidence of having any angular motion. The particles just seemed to inherently have this angular momentum, as if they were spinning like a top on their axis. Additionally, these particles would only be "spinning" with particular speeds - no faster, and no slower. This suggested that Spin was quantized - it could only take specific values. The particles could, however, spin in opposite directions. This mysterious particle property was called "spin".

(It's worth noting that particles could also gain additional angular momentum by the conventional classical means - moving along a curved path for example. But this angular momentum was added on top of the inherent Spin angular momentum the particle already had).

When Dirac came up with his famous equation, spin seemed to fall out naturally from the mathematics. Particles following the Dirac Equation needed to have this inherent angular momentum, that was not caused by any particular spinning or orbiting or anything like that. And Dirac's math suggested the Spins were also quantized just the right way (remember they could only "spin" at certain speeds, as observed experimentally).

The Dirac equation actually took into consideration Special Relativity as well as Quantum Mechanics. This suggests that Spin is a Special Relativistic effect, but this is not quite true - particles do not need to be moving at relatively high velocities in order to have Spin.

You may have heard particles being described as "Spin-1/2" (e.g. electrons) or "Spin-1", e.g. photons. In this video, we discuss what that means. We see how we can find the number of possible Spin measurement results each particle has, depending on its Spin number. We also see how we can find the exact angular momentum each particle has in each of its Spin states.

Lastly, we see that particles with half-integer spin are known as fermions, and particles with integer spin are known as bosons. These two classes of particle behave very differently to each other!

If you're unsure about how particles behave when multiple spin measurements are made on it in different directions, then I'd suggest reading up about wave function collapse and the Heisenberg Uncertainty Principle.

Thanks very much for watching - I hope this discussion of Spin in Quantum Physics was useful!

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0:00 - Intro
0:30 - What is Spin? Angular Momentum Discussions!
1:16 - Spin as Inherent Angular Momentum - Particles just kinda... have it?!
1:51 - Where does Spin come from? Special Relativity and the Dirac Equation... ish
2:35 - The Spin of an Electron: Spin Up and Spin Down
3:33 - Big thanks to our sponsor, Skillshare - free trial at the link in the description!
4:30 - How do we know electrons are "spinning" but not really? Stern Gerlach Experiment!
4:56 - Measuring the spin of an electron, Heisenberg Uncertainty Principle, Wave Function Collapse
6:21 - Spin Is Quantized! It can only take specific values :O
7:26 - Spin 1/2 and Spin 1 particles - what does this mean?
7:56 - How Spin Number gives all the spin states of the particle - with Reduced Planck Constant
8:13 - Finding all the Spin states of an Electron (Spin-1/2)0
9:16 - Finding all the Spin states of a Photon (Spin-1)
10:06 - Finding all the Spin states of a generic Spin-3/2 particle
10:34 - Fermions (half-integer spin) and Bosons (integer spin) - classes of particle!
11:08 - Thanks for watching! Check out my socials :)

Видео Spin in Quantum Mechanics: What Is It and Why Are Electrons Spin 1/2? Physics Basics канала Parth G