What is spin in quantum mechanics?

 Quantum mechanical spin is basically intrinsic angular momentum which every elementary particle and composite particle possesses. There are two terms to be explained. First- intrinsic. Intrinsic property is a property which the object referred to possesses by itself, it is inherent where as an extrinsic property is something which is not inherent. For instance, mass is an intrinsic property whereas weight is an extrinsic property. Just like mass, charge and spin are also intrinsic properties. Second term to explain is angular momentum. So, what is momentum? By the term momentum, we simply mean linear momentum which is something an object possesses when it moves along a straight line.

Linear momentum = mass * velocity, or simply, p = mv

Formula of linear momentum
Note: those arrows signify that they are vectors

Angular momentum is something which an object possesses when it spins on its axis or around any object.

Angular momentum = mass * tangential velocity * radius of rotation, or simply, L = mvr = pr

(where p is linear momentum)

Formula of angular momentum
Arrows signifying the vectors

But the craziest thing about quantum mechanics is that some particles seem to possesses inherent angular momentum. It is not caused by the particles spinning on its own axis. But it seems as if they are spinning, and that is why the name "spin".

This so called "intrinsic angular momentum" or "spin" creates an "intrinsic" or "inherent" magnetic field around a charged particle like electron, an "intrinsic magnetic moment" is created, as if the particle is actually spinning. Just like when a charge revolves in a circle, it creates a magnetic field like a bar magnet. So, spin causes charged particles to be tiny bar magnets.

Spinning charges or current creating a magnetic field just like a bar magnet

Magnetic field due to a bar magnet

Visualization of spin of electron creating magnetic moment

But how do we know about "spin" in the first place. Well, it was first detected in an experiment called the Stern-Gerlach experiment in the year 1922. I would highly recommend to check out that experiment once you finish reading this blog.

But where does this so called "spin" come from. It was first predicted by the famous British physicist Paul Dirac when he combined special relativity with quantum mechanics and gave us the famous Dirac equation. I will surely write a blog on this topic later on.

The Dirac equation also predicted the presence of anti-matter

Now, let's come to quantization of spin. Yeah, you read it right. Spin is also quantized in quantum mechanics.

"Spin" or "intrinsic angular momentum" of each particle can take only certain allowed values which are either integral or half-integral multiples of the reduced Planck constant which is denoted by ħ.

ħ = h/2π, where h = Planck constant ≈ 6.62607004 * 10^-34 J.s

Particles with spin values that are integral multiples of ħ are called bosons and particles with spin values that are half integral multiple of ħ are called fermions.

But how many spin values can a particle take?

Well say a particle is a spin-n particle where n denotes the maximum multiple of ħ which the particle's spin can take. Now keep reducing 1 from n until you reach negative n. Now count the number of spin value it takes.

For example, say a particle is a spin-1 particle. So, the possible values of spin are 1, 0, -1 (times ħ). Or say a particle is a spin-3/2 particle, then, the possible values of spin are 3/2, 1/2. -1/2, -3/2 (times ħ).

Thanks for keeping the patience to read this blog😊😊.