Quantum Spin (3) - The Bloch Sphere

[Undergraduate Level] - In my third video on quantum spin, I discuss how all quantum spin states can be thought of as vectors on the Bloch Sphere. Each quantum spin state is the eigenstate of a spin measurement in some direction.

[puzu]

I cant thank you enought. This is exactly the "entry level" course to QM/spin I've been searching for. I ve taken a lot of classes online (CS-Student), but only since a short period of time I am able to grasp the math behind it and there are a lot of "introductionary" courses out there. But when you start them it goes from 0 to 100 like in no time and you completely lose it. Here it's completely different. Due to the pure mathematical view here it's so much easier to build a fundamental understanding. And the way you are explaining is fascinating, it's not hard to see that you are really puting yourself in the position of students who want to learn that topic and you DO the neccecary calculations so it stays in the head - instead of doing just 1 example and go on like most profs do. I REALLY APPRICIATE THAT. This tought me more in 1 lecture than some MIT-courses in 4.

Man, you did a nice job, your work brings me joy. I m looking forward to watch more of your lectures.

[mastercheif]

You are the best teacher in quantum mechanics.my humble respect

[sahhaf]

I think te correct expression of the question in @13:35 is this:
How can we express arrow_n state in up-arrow_z and down-arrow_z basis?
Phytsically, this correspond to a (1) measurement along n, and getting up-arrow_n (2) and then, doing a measurement along z.

[tanchienhao]

Wonderful video! A lot of books lack these steps in check to make sure the math is consistent and you covered it perfectly

[datsmydab-minecraft-and-mo]

What a fantastic video! you explain things step by step and in such a simple manner!

[ecdavek]

Kewl .. I'm slowly going through my first pass of this series on spin. Really enjoy and appreciate both your rigor and love of drilling on basics. No just plopping down a relation and saying - ok here's it is, lets moves on, but rather working through proof that relation is correct and for each component ( direction ) . Also your providing little tips about different identities or matrix manipulations etc shows to me you have a real respect for those who will be viewing your work . So let me add my " Thanks for doing these, very much appreciated " to the similar comments already posted.

I've wanted to get a good understanding of entanglement and Bell's theorem for a long time. I suspect this series will finally give me the mathematical foundation for doing that. So . hot dog !

[sankaranv]

I love this video! I'm taking a class on Quantum Information and this was very helpful in understanding rotations and operators.

[ericsmathmoments]

Noah, thank you for your charming and helpful videos on some of my favorite topics on physics and the interface between physics and math. I have landed on your videos a few times because of shared interests. And I really have to ask you if any of your thousands of viewers have ever pointed out that your voice is a dead ringer (if one can apply that term to voices) for Josh Clark, co-host of the hugely popular and enduring podcast "Stuff You Should Know". My experience would lead me to expect that you would maybe be the last to notice this because everyone hears their own voice differently than others hear it. Hope you are doing well.

[pushpendrakumar-onpj]

Great explanation....i have seen till now the matrices....💐💐🙏🙏

[swan]

Thank you very much for ur time and effort. ur videos are really helpful, I think I gotta watch all of them 👍 Plz upload more

[sahhaf]

@4:40 when up arrow along the direction n hat is written as a two component vector representation, what is the basis that we use?

[ashutosh_kumar_kashyap]

You did best, , I was searching for this one

[yasama-vv]

This was so useful, you are a life saver, thanks a lot ✨

[x-jw]

my favorite part was when you said "in this video i will be talking."

[kafianan]

At 37:40 .. didn't understand how e^(-iy) came.. can anyone explain how the negative sign came?

[yyc]

When I watch it again, I found myself not quite clear at around 9:43. Initially, I thought the σx and σy are just arbitrary names Pauli gave to these matrices (we can also call them σ1 and σ2 right?). I mean, what if we switch the order of σx and σy, then the following dot product of n·σ will also be changed (=nxσy + nyσx + nzσz). Where am I wrong? Thanks.

[tapmoron]

Not the way i would present the matter. Indeed a quantum state with 2 fundamental states (often called a qbit) is a vector of C² with norm 1. But since the global phase is irrelevant (as long as we do not consider possible entanglement with others state) we can instead of v represent exp(i theta ) v . So indeed instead of representing any vector v=(a, b) in C^2 with lv|² =a^2 +b^2=1 we may choose a to be not only real be a positive real, and b can be chosen to be a posive number time a phase.

So doing you write any state as:

S= cos(theta/2) | spin up > + sin(theta/2) exp(i phi )
so you get two angle, theta is in [0, pi] and phi in [0, 2pi] .

Indeed theta/2 is such that both its cosinus and sinus are posiive.

So angle theta= 0 represent the state Spin UP, the angle theta=pi correspond to SPIN Down.

For the angle theta=pi/2 we get both cos(pi/4) and sin pi/4 and the state will 1/sqrt(2) ( SpinUp + exp(iphi) SpinDown

and so on.

[yyc]

9:30 why the dot product n·σ does not have the crossing terms such as n_x·σ_y ?

[zdayz]

... ya... 'modified rodrigues parameters' encoding a direction vector as two angles doesn't simplify the situation... just get lots of sin-sin and sin-cos sort of products, and none of the terms cancel out.... working with projections on the axii (1, 0, 0), (0, 1, 0), (0, 0, 1) gives you a lot of zeros that drop out terms. Although it does seem to work for you since you can leave phi as a phase.... but really you can treat every axis' view of the spin the same as the Z using the spin vectors in rotation space... turns out the sin(?) some component of the normal is also an angle(?) ... with theta and phi you only have 2D of freedom... and in rotation space (x, y, z) are three angles anyway, and isn't 3 better than 2? :) It's a lot better than 4?

[terrencelau]

I don't understand with sanity checks