I am a PhD student from China, and my research direction is quantum information. I really like listening to your program, which is very clear. I hope you can stick to it, thank you!
I'm currently studying advanced quantum mechanics as part of my master's degree, and your videos have been incredibly helpful to understand and clarify fundamental concepts and mathematical procedures. Seriously, keep on doing this excellent job, greetings from Venezuela! 🔥
Thank you Professor M! I've watched ALL your videos and they are super helpful! The reason I love your videos the most is that every step in the equation derivation is super clearly stated, no jump of item cancellation or substitution. Looking forward to the Rabi Oscillation as mentioned at the beginning of this video!
I have now watched all 84 of your videos from beginning to end. They are one of the best set of videos on QM on UA-cam. Please keep going. There is so much more to teach and you guys are so good and clear. Please produce many many more. ❤❤❤
Thanks for your support! We do plan on producing many more videos, and (after a rather long pause), we'll actually publish a new one this coming Monday! It will cover the energy eigenvalues of 2-state systems, hope you like it! :)
As a layman, there's one thing I would like to know. Maybe it's a bit off-topic, but in short: In geometry, If you shift a vector along x direction and then y, you get the same result as, shift y fist and then x. So, xy = yx --> xy-yx = 0 --> Flat space If xy ≠ yx --> xy-yx ≠ 0 --> Curved Space. Has the commutator of quantummechanical Operators [X,Y]=XY-YX something to do with curved spaces?
Hello, I cherish your contribution. The proof the Pauli Matrices forms a bases on M2(C) maybe a more direct and cleaner approach would be using the inner product < O(i), O(j) > = d(i,j) ? Respectfully.
Hi, do you guys plan on doing a video on 3-D scattering/Born approximation? The math is getting to me, I liked the spherical harmonics video because it helped me understand the mathematics behind it.
So if we were to derive that density matrix ρ can be written in terms of the Pauli matrices in the form ρ = (1/2) (σ0 +a·σ),with a : a vector of real coefficients a = (ax ,ay ,az ) were we to start with the general expression you showed?
We like a range of textbooks for quantum mechanics (the motivation behind describing this topic), which include those by Sakurai, Shankar, Cohen-Tannoudji, and Merzbacher. I hope this helps!
@@Jagann I usually see it covered in physics textbooks, usually when 2-state quantum systems are discussed. As an example, Cohen-Tannoudji has a good overview on this point. Not sure of any maths textbooks that do cover it...
Hello profs, it'd be great if you could do a video on the famous Bell Inequalities as well I was surfing through your playlist but couldn't find one :) Best Wishes!
and what about a generic 2x2 matric that can be written only in a linear combination of the Pauli matrices? Im stuck in an excercise where they give you that and then ask for a basis of orthonormal eigenvectors for that generic one (in relation to the standard hermitian product)
We prove in the video that this is necessary when the 2x2 matrix is Hermitian, otherwise the expansion coefficients will in general be complex numbers. I hope this helps!
I am a PhD student from China, and my research direction is quantum information. I really like listening to your program, which is very clear. I hope you can stick to it, thank you!
Glad you like it, and good luck with your PhD! What university are you working at?
I'm currently studying advanced quantum mechanics as part of my master's degree, and your videos have been incredibly helpful to understand and clarify fundamental concepts and mathematical procedures. Seriously, keep on doing this excellent job, greetings from Venezuela! 🔥
Great to hear!
Thank you Professor M! I've watched ALL your videos and they are super helpful! The reason I love your videos the most is that every step in the equation derivation is super clearly stated, no jump of item cancellation or substitution. Looking forward to the Rabi Oscillation as mentioned at the beginning of this video!
Thanks for watching, and glad you find our approach useful! :)
Thank you -- even for a basic topic, your clarity and precision is very helpful!
Glad this was helpful!
I have now watched all 84 of your videos from beginning to end. They are one of the best set of videos on QM on UA-cam. Please keep going. There is so much more to teach and you guys are so good and clear. Please produce many many more. ❤❤❤
Thanks for your support! We do plan on producing many more videos, and (after a rather long pause), we'll actually publish a new one this coming Monday! It will cover the energy eigenvalues of 2-state systems, hope you like it! :)
Another piece of great work!
Glad you also like this one! :)
Please give us more videos in your wonderful interpretations! Eagerly looking for a series on statistical mechanics!
Sorry we've been too busy lately with work, but we really are aiming to keep this up!
@@ProfessorMdoesScience certainty, waiting for this eagerly
You have such a nice handwriting! :)
Thanks! :)
After a long wait.....and as usual liked the video first and then watched it ...... learned from it
Great! :)
Very good and simple intro to QM. Please continue your work!
Thanks for your support! :)
I like your videos. I find them useful and overall content applicable in my advanced quantum mechanics course, which I'm working on
Glad to hear; may we ask where you are studying?
Thanks this helped a lot I am in quantum now
Glad you found it useful!
Wish to see more from your brilliant channel
Thanks for your continued support!
As a layman, there's one thing I would like to know. Maybe it's a bit off-topic, but in short:
In geometry, If you shift a vector along x direction and then y, you get the same result as, shift y fist and then x.
So, xy = yx --> xy-yx = 0 --> Flat space
If xy ≠ yx --> xy-yx ≠ 0 --> Curved Space.
Has the commutator of quantummechanical Operators [X,Y]=XY-YX something to do with curved spaces?
Hello, I cherish your contribution. The proof the Pauli Matrices forms a bases on M2(C) maybe a more direct and cleaner approach would be using the inner product < O(i), O(j) > = d(i,j) ? Respectfully.
Thanks for the suggestion!
Hi, do you guys plan on doing a video on 3-D scattering/Born approximation? The math is getting to me, I liked the spherical harmonics video because it helped me understand the mathematics behind it.
Scattering has been on our to-do list for a while, we hope to get there soon...
So if we were to derive that density matrix ρ can be written in terms of the Pauli matrices in the form ρ = (1/2) (σ0 +a·σ),with a : a vector of real coefficients a = (ax ,ay ,az ) were we to start with the general expression you showed?
Great video. Any textbooks you would suggest for reference?
We like a range of textbooks for quantum mechanics (the motivation behind describing this topic), which include those by Sakurai, Shankar, Cohen-Tannoudji, and Merzbacher. I hope this helps!
I was checking for this particular topic
@@Jagann I usually see it covered in physics textbooks, usually when 2-state quantum systems are discussed. As an example, Cohen-Tannoudji has a good overview on this point. Not sure of any maths textbooks that do cover it...
Hello profs, it'd be great if you could do a video on the famous Bell Inequalities as well I was surfing through your playlist but couldn't find one :) Best Wishes!
Thanks for the suggestion, it's on our to-do list!
and what about a generic 2x2 matric that can be written only in a linear combination of the Pauli matrices? Im stuck in an excercise where they give you that and then ask for a basis of orthonormal eigenvectors for that generic one (in relation to the standard hermitian product)
We'll cover the eigenvalues and eigenvectors of a general 2x2 matrix in the next two videos, so stay tuned! 🙂
Can u upload the video on spin half
We are working on a spin-1/2 series, but it may still take some time... stay tuned! :)
Why do the expansion coefficients have to be real?
We prove in the video that this is necessary when the 2x2 matrix is Hermitian, otherwise the expansion coefficients will in general be complex numbers. I hope this helps!