2x2 matrices in terms of Pauli matrices

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  • Опубліковано 10 лис 2024

КОМЕНТАРІ • 45

  • @linshuaizhang6158
    @linshuaizhang6158 Рік тому +6

    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!

    • @ProfessorMdoesScience
      @ProfessorMdoesScience  Рік тому

      Glad you like it, and good luck with your PhD! What university are you working at?

  • @victorquantum6586
    @victorquantum6586 Рік тому +9

    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! 🔥

  • @yiheyao2859
    @yiheyao2859 Рік тому +4

    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!

  • @richardthomas3577
    @richardthomas3577 Рік тому +4

    Thank you -- even for a basic topic, your clarity and precision is very helpful!

  • @YossiSirote
    @YossiSirote Рік тому +2

    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. ❤❤❤

    • @ProfessorMdoesScience
      @ProfessorMdoesScience  Рік тому +2

      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! :)

  • @LifeIzBeautiful10
    @LifeIzBeautiful10 Рік тому +2

    Another piece of great work!

  • @paulbk2322
    @paulbk2322 Рік тому +2

    Please give us more videos in your wonderful interpretations! Eagerly looking for a series on statistical mechanics!

    • @ProfessorMdoesScience
      @ProfessorMdoesScience  Рік тому

      Sorry we've been too busy lately with work, but we really are aiming to keep this up!

    • @paulbk2322
      @paulbk2322 Рік тому +1

      @@ProfessorMdoesScience certainty, waiting for this eagerly

  • @Tibug
    @Tibug Рік тому +4

    You have such a nice handwriting! :)

  • @paulbk2322
    @paulbk2322 Рік тому +1

    After a long wait.....and as usual liked the video first and then watched it ...... learned from it

  • @TopConductor
    @TopConductor 11 місяців тому +1

    Very good and simple intro to QM. Please continue your work!

  • @cosmotheorist
    @cosmotheorist Рік тому +1

    I like your videos. I find them useful and overall content applicable in my advanced quantum mechanics course, which I'm working on

  • @someguy3104
    @someguy3104 Рік тому +1

    Thanks this helped a lot I am in quantum now

  • @paulbk2322
    @paulbk2322 Рік тому +1

    Wish to see more from your brilliant channel

  • @Handelsbilanzdefizit
    @Handelsbilanzdefizit Рік тому +2

    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?

  • @DanielStJohn-hc7mh
    @DanielStJohn-hc7mh Місяць тому +1

    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.

  • @ruifenghuang1029
    @ruifenghuang1029 Рік тому +1

    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.

    • @ProfessorMdoesScience
      @ProfessorMdoesScience  Рік тому

      Scattering has been on our to-do list for a while, we hope to get there soon...

  • @TheHoodedMan21
    @TheHoodedMan21 Рік тому

    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?

  • @Jagann
    @Jagann Рік тому +1

    Great video. Any textbooks you would suggest for reference?

    • @ProfessorMdoesScience
      @ProfessorMdoesScience  Рік тому +1

      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
      @Jagann Рік тому +1

      I was checking for this particular topic

    • @ProfessorMdoesScience
      @ProfessorMdoesScience  Рік тому

      @@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...

  • @achalvinod7097
    @achalvinod7097 Рік тому +1

    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!

  • @felipevidalekelund1451
    @felipevidalekelund1451 Рік тому +1

    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)

    • @ProfessorMdoesScience
      @ProfessorMdoesScience  Рік тому

      We'll cover the eigenvalues and eigenvectors of a general 2x2 matrix in the next two videos, so stay tuned! 🙂

  • @sanskarnanda6604
    @sanskarnanda6604 10 місяців тому +1

    Can u upload the video on spin half

    • @ProfessorMdoesScience
      @ProfessorMdoesScience  10 місяців тому

      We are working on a spin-1/2 series, but it may still take some time... stay tuned! :)

  • @datho1314
    @datho1314 11 місяців тому +1

    Why do the expansion coefficients have to be real?

    • @ProfessorMdoesScience
      @ProfessorMdoesScience  11 місяців тому

      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!