[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.
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.
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 !
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.
... 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?
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.
@ 3:22 Great explanation: "You can see". Here is another person who does not understand the difference between "having knowlegde" and "transferring knowledge".
dude that's like the most basic thing in spherical coordinates which is learned in the first year in every Physics Degree. You can't expect someone to explain a concept of quantum mechanics and build all the mathematical knowledge required up to that point in that same video. Some foundations are mandatory before you get to these complex topics. And again, what he did was just a change of coordinatess between cartesian and spherical, nothing too fancy.
@@jacobvandijk6525 no dude, I'm sorry, I don't want to sound mean but what you are asking is not only impossible but it is also really inefficient. If you want to see a video on intermediate quantum mechanics you have to know basics mathematics. If you watch a video about the bloch sphere, I think it's common sense to at least know how to represent a point in a sphere. Plus, in the time you wrote the first comment, you could just have search in Wikipedia the article about spherical coordinates.
The "dot product" notation used in this video is supposed to mimic the regular dot product between two vectors. If you have two vectors v = (v_x, v_y, v_z) and w = (w_x, w_y, w_z), then the dot product is v · w = v_x * w_x + v_y * w_y + v_z * w_z with no "cross terms."
