Just pointing out since youtube has auto-generated video chapters. The sigma are called the "Pauli matrices", NOT the "polymatrices" as the caption algorithm has referred to them as. Just to clear up any potential confusion for newcomers.
Thanks so much! I'm taking my quantum final in a few hours.. graduating in 2 days!! You have been such an amazing help, I appreciate your time! Blessings to you, Brant Carlson!
Congratulations! I’m assuming you graduated with a BS in physics? Just out of curiosity, what field did you end up going into? I’m graduating in about 6 months with a physics BS as well and am a bit worried about job opportunities.
@@JoeySalinas12 go to grad school, if gpa is low, stay for few semesters longer to take some computer science courses. with BSc in Physics alone, job prospects are limited
@@blackcohn Oof, thanks for that reality check. Currently applying to grad schools, but i'm a bit worried about my chances of getting in anywhere. I might have to take your suggestion and stay for an extra year in undergrad.
@@nidhishsharma9471 Ended up not getting into graduate school, but instead landed a job working as a data analyst. I gotta say, there are plenty of job opportunities for a physics grad if you don't mind going into tech/business and learning a few new skills. This is especially true if you were able to take part in some research during undergrad
Clarity: 10 Conciseness: 10 Unambiguity: 10 Narration style: 10 BTW this rating system would apply to every video in this series. Some of the explanations are so clear it leaves you wondering 'Why didn't I think of that'? There is other material that may be as informative here on TH-cam...but they typically are at least twice as long and don't seem to be as easy to follow in a step by step fashion. BTW, the Sx and the Sy operators expressed in the S+ and S- fashion seem to uncannily resemble the Euler exponential expressions for cosine and sine respectively. It it naive to think that they are more than casually related, especially since in polar coordinates the Cartesian x is a function of cosine and the y is a function of sine? Furthermore S+ seems to mirror e^ix while S- seems to be patterned after e^-ix. A brief search does not seem to support this.
I am so glad I found this video. My mathematician brain finds topics so much more intuitive when in matrix form. It then gets even better by involving eigen stuff. If anyone is reading this the characteristic polynomial, who's zero are the eigen values, for a 2×2 matrix A is always: C(x) = x²-trace(A)x+det(A) Note: I used x since I can't type lambda in the comment.
Check your understanding: . . . 1. Eigenvalue of Sy : hbar/2 and -hbar/2 ( just like Sx and Sz ) 2. Eigenvectors of Sy: y_plus = 1/sqrt(2) * ( 1, i ) # with eigenvalues hbar/2 y_minux = 1/sqrt(2) * ( 1, -i ) # with eigenvalues -hbar/2 3. x_plus state can be expressed in Sy eigenstates, as x_plus = ( 1/2 - i/2) * y_plus + ( 1/2 + i/2 ) * y_minus. So the possibilities is both 0.5 to attain one of the states of corresponding eigenvalue. 4. Same as before, 0.5 possibility to get both states and corresponding eigenvalues.
Check your understanding +/- 1, (1 -i), (1 i). I think it's 50 50 on |up> and |down>, but I think this is more a guess than anything. Someone let me or others know what 3) and 4) are supposed to be answers please, thanks!
So wait, there is no representation of spin in Psi(x, t) or Psi(r, theta, phi) at all? What were we going on about in the hydrogen atom if electrons have half integer spin and can't be in those integer L configurations? Please tell me SOMETHING about spin lives in the wavefunction Psi(x, t)
@Dr Deuteron I'm not totally getting it, but thanks! I'm trying to learn tensors at 36 without ever having taken linear algebra, so go easy on me. Can you explain why we need multiple components to express spin? What are the rows really representing physically?
@Dr Deuteron thanks for the explanation man! So for spin 1/2 SU(2) is a 2D symmetry including complex rotations? And psi(x) in that case has two forms that are some combination of spatial and phase rotations of each other? Is that right?
@Dr Deuteron what are the basis vectors of the [cos theta/2, sin(theta/2) exp(i phi)] vector? An abstract vector space of the "Bloch sphere"? Or spatial axes? Or basis wavefunctions?
@Dr Deuteron Thanks for taking the time to explain this to me! I already get it at the mathematical level, I just can't wrap my head around it on the physical level. There has to be some asymmetry or antisymmetry of the particle or its coupled fields in real space, right? Otherwise it would be unobservable. All I want to know is what that asymmetry or antisymmetry is. Is there a phase correlation with (real spatial) theta or phi or t? Or d/dt of those? How does the A field know that it needs to circularly polarize photons to conserve angular momentum? Or any other conservation of angular momentum? What is the relationship between the Bloch sphere and real space? Is projected onto real space? Does a single particle just "know" its position on the sphere, or does it have a wavefunction over Bloch space? Are there dynamics to that, or conserved quantities?
Just pointing out since youtube has auto-generated video chapters. The sigma are called the "Pauli matrices", NOT the "polymatrices" as the caption algorithm has referred to them as. Just to clear up any potential confusion for newcomers.
Thanks so much! I'm taking my quantum final in a few hours.. graduating in 2 days!!
You have been such an amazing help, I appreciate your time!
Blessings to you, Brant Carlson!
Congratulations! I’m assuming you graduated with a BS in physics? Just out of curiosity, what field did you end up going into? I’m graduating in about 6 months with a physics BS as well and am a bit worried about job opportunities.
@@JoeySalinas12 go to grad school, if gpa is low, stay for few semesters longer to take some computer science courses. with BSc in Physics alone, job prospects are limited
@@blackcohn Oof, thanks for that reality check. Currently applying to grad schools, but i'm a bit worried about my chances of getting in anywhere. I might have to take your suggestion and stay for an extra year in undergrad.
@@JoeySalinas12 how did it go for you?
@@nidhishsharma9471 Ended up not getting into graduate school, but instead landed a job working as a data analyst. I gotta say, there are plenty of job opportunities for a physics grad if you don't mind going into tech/business and learning a few new skills. This is especially true if you were able to take part in some research during undergrad
Clarity: 10
Conciseness: 10
Unambiguity: 10
Narration style: 10
BTW this rating system would apply to every video in this series. Some of the explanations are so clear it leaves you wondering 'Why didn't I think of that'?
There is other material that may be as informative here on TH-cam...but they typically are at least twice as long and don't seem to be as easy to follow in a step by step fashion.
BTW, the Sx and the Sy operators expressed in the S+ and S- fashion seem to uncannily resemble the Euler exponential expressions for cosine and sine respectively. It it naive to think that they are more than casually related, especially since in polar coordinates the Cartesian x is a function of cosine and the y is a function of sine? Furthermore S+ seems to mirror e^ix while S- seems to be patterned after e^-ix. A brief search does not seem to support this.
+Ron Toolsie I was thinking the same thing regarding the ladder operators and Euler formula.
Nice observation but not really.
Thanks a lot for these clear, concise and often humorous video's! Really helped me out on some fundamental understanding.
I am so glad I found this video.
My mathematician brain finds topics so much more intuitive when in matrix form.
It then gets even better by involving eigen stuff.
If anyone is reading this the characteristic polynomial, who's zero are the eigen values, for a 2×2 matrix A is always:
C(x) = x²-trace(A)x+det(A)
Note: I used x since I can't type lambda in the comment.
I love you. This helped me TREMENDOUSLY on my homework.
Wish you went past chapter 5! Thank you for this
That my sir is an excellent explanation of spin.
Check your understanding:
.
.
.
1. Eigenvalue of Sy : hbar/2 and -hbar/2 ( just like Sx and Sz )
2. Eigenvectors of Sy:
y_plus = 1/sqrt(2) * ( 1, i ) # with eigenvalues hbar/2
y_minux = 1/sqrt(2) * ( 1, -i ) # with eigenvalues -hbar/2
3. x_plus state can be expressed in Sy eigenstates, as
x_plus = ( 1/2 - i/2) * y_plus + ( 1/2 + i/2 ) * y_minus.
So the possibilities is both 0.5 to attain one of the states of corresponding eigenvalue.
4. Same as before, 0.5 possibility to get both states and corresponding eigenvalues.
great video it helped me a lot to understand quantum mechanics
Thank you so much. You explained all of this in such a clear way.
Thank you very much for this great explanation!!!
Check your understanding
+/- 1, (1 -i), (1 i).
I think it's 50 50 on |up> and |down>, but I think this is more a guess than anything. Someone let me or others know what 3) and 4) are supposed to be answers please, thanks!
I forgot to normalize the eigenvectors! Normalized, they'll have a 1/sqrt(2) constant attached to (1 -i) and (1 i).
Very informative and easy to follow, thanks!
Very good explanation, Thank you very much
thx for the video ... was really good & helpful
Muy buena explicación. Estaría perfecto que hables sobre el electrón en un campo magnético
What are the normalized eigenvalues of Sy? I found the unnormalized eigenvalues of Sy are (1 i) and (1 -i)
normalised eigenvectors of Sy are 1/√2[-i 1] and 1/√2[i 1].
Thank you very much! It's really helping me.
Btw: had to set it to 0.75 speed 😂
When will you release the Spin 2/2 video?
Excellen lecture....
Very clear, thx
Just excleent...why in mit when they teach they jump so much in front of the board I don't understand them
Thank you man
how to understand spin x and spin y are not hermitian, they are not observable.
LOT OF THANKS BUT SAME AS IN BOOK IT IS NOT MUCH FOR CONCEPTUAL STUDY .
So wait, there is no representation of spin in Psi(x, t) or Psi(r, theta, phi) at all? What were we going on about in the hydrogen atom if electrons have half integer spin and can't be in those integer L configurations? Please tell me SOMETHING about spin lives in the wavefunction Psi(x, t)
@Dr Deuteron I'm not totally getting it, but thanks! I'm trying to learn tensors at 36 without ever having taken linear algebra, so go easy on me.
Can you explain why we need multiple components to express spin? What are the rows really representing physically?
@Dr Deuteron thanks for the explanation man! So for spin 1/2 SU(2) is a 2D symmetry including complex rotations? And psi(x) in that case has two forms that are some combination of spatial and phase rotations of each other? Is that right?
@Dr Deuteron what are the basis vectors of the [cos theta/2, sin(theta/2) exp(i phi)] vector? An abstract vector space of the "Bloch sphere"? Or spatial axes? Or basis wavefunctions?
@Dr Deuteron Thanks for taking the time to explain this to me!
I already get it at the mathematical level, I just can't wrap my head around it on the physical level. There has to be some asymmetry or antisymmetry of the particle or its coupled fields in real space, right? Otherwise it would be unobservable. All I want to know is what that asymmetry or antisymmetry is. Is there a phase correlation with (real spatial) theta or phi or t? Or d/dt of those?
How does the A field know that it needs to circularly polarize photons to conserve angular momentum? Or any other conservation of angular momentum?
What is the relationship between the Bloch sphere and real space? Is projected onto real space? Does a single particle just "know" its position on the sphere, or does it have a wavefunction over Bloch space? Are there dynamics to that, or conserved quantities?
thank you sir
hi zahir..what is ur field of studies