**Errata**: 5:55 The result of the integral should be -3E*sqrt(3), sorry for that! You can easily compute this integral using Python: ######## import sympy as sy from sympy.physics.hydrogen import Psi_nlm as psi r, theta, phi = sy.symbols(r'r \theta \varphi') psi_310c = psi(3,1,0,r,phi,theta).conjugate() psi_320 = psi(3,2,0,r,phi,theta) jacobian = r**2 * sy.sin(theta) sy.integrate(psi_310c * r*sy.cos(theta)* psi_320 * jacobian, (r,0,sy.oo), (theta,0,sy.pi), (phi,0,2*sy.pi)) ########
I am working my way through grad school; yet this short video is the first time I learned what Wigner-Eckart theorem really means. Thanks a lot. You made my day :-)
We're glad to hear that, thanks for your comment! The Wigner-Eckart theorem was also something that confused us a bit, so we thought that's a great topic for a video!
While preparing some material for a course I'm teaching, I stumbled upon this beautiful channel and its clear and visual explanations. Really good stuff. Certainly gonna recommend it to my colleagues and students. Keep it up.
Hare Krsna, this is awesome! Thank you for the clean and straightforward presentation, and for adding a nice, simple example at the end, a real easter treat for me right now :)
This is so funny because I just went over the C-G Theorem in quantum 3 but this is much more helpful. Edit: ok actually I saw this in quantum 1, but it was nice too see it again in here.
Hello! in 1:00, you wrote |jm> as tensor product! But how can this be true? Since they(j,m) both live in a same hilbert space, tensor product seems to be just wrong. Also my professor told me that |jm> is not a tensor product between |j> & |m>..
When solving the simplest case at 5:13 - where does the radial part of the electric field go? E = Ez = Ercos(\theta). Is all the radial dependence incorporated into the inner product for the ket state n=3?
z is part of a vector: (x,y,z). Therefore, the rank is 1, that's basically the definition of what a vector is. Next, in the spherical basis, you can write the position vector r like this: r_+ = x + i y r_0 = z r_- = x - i y Therefore, z is exactly the 0-component of the rank-1 tensor r!
Hi, Thank you a lot! I was wondering about the radial part of function where you said its 1 should I calculate it for another state? I asking that because you here said = 1 thanks again!!
Since \hat z = cos(theta) did not depend on r, there was no need to write the radial part of the wave function in its position basis in order to integrate it. If, however, the operator would have been r^2 (or something similar), we would have had to write |3> as and integrate over r. But since every r-dependence was inside the |3>, we were able to make use of the orthogonality of R_n(r) and simply write = 1. Hope this helps!
@@PrettyMuchPhysics How is $E \hat z$ the relevant operator in this condition instead of $Ez$. Won't the latter tell us about the matrix elements of the perturbation? Let's say we are doing degenerate perturbation theory.
This matrix element is for instance important in calculating the Stark effect. There, you have an electric field, which leads to an additional potential in the Hamiltonian. This electric field generates a potential by coupling to the electric dipole moment, which is proportional to \vec r. Therefore, the product of E and r is interesting, which simplifies to E z if E only points in z-direction.
The index order does not really matter, but yes, unfortunately it‘s inconsistent with what we wrote in the top right corner. Thanks for letting us know!
I’m pretty new in this stuff so sorry if this is a silly question: how can you go from Y_10 to T_0^{1}? i.e. how can a function be equal to a tensor? I have learned that any Cartesian rank 2 tensor, say a 3x3 matrix, can be decomposed into irreducible representation basis (irreps) using rank-0,1,2 spherical tensors; are these tensors the same as those mentioned in this video ( T_q^k)? And how, please? Thanks a lot!🙏 🙏🙏
I am assuming you're referring to the part around 06:10. It might be a bit sloppy, but the important thing is, that we start with an operator (z) and end with an operator (T^(1)_0). The part in the middle is there to show you that z indeed behaves like Y_10, and since the spherical harmonics are a basis, z can only be represented by a spherical tensor (T) with the same lm as Y_10. Therefore we identify z with (1)
Hi PMP! I want to calculate reduced matrix elements for H2 molecule using python......is ther any way to do so...... I have calculated wave function matrix for H2, can i use it to calculate reduced matrix elements.....
Within the scope of the Wigner-Eckart theorem, you get the reduced matrix element by doing a full calculation first, and then diving by the Clebsch-Gordan coefficient.
Good question, I don't know why we forgot about that, the "r" should be included 🙈 Fortunately, this only affects the numerical value at the end, so instead of 2/sqrt(15) you'd get some different number. Thanks for letting us know!
**Errata**:
5:55 The result of the integral should be -3E*sqrt(3), sorry for that! You can easily compute this integral using Python:
########
import sympy as sy
from sympy.physics.hydrogen import Psi_nlm as psi
r, theta, phi = sy.symbols(r'r \theta \varphi')
psi_310c = psi(3,1,0,r,phi,theta).conjugate()
psi_320 = psi(3,2,0,r,phi,theta)
jacobian = r**2 * sy.sin(theta)
sy.integrate(psi_310c * r*sy.cos(theta)* psi_320 * jacobian, (r,0,sy.oo), (theta,0,sy.pi), (phi,0,2*sy.pi))
########
One of the best ways to invest 10 minutes of my life as a physics student. :)
Haha, that‘s a very kind comment!
This educator is phenomenal. Laying it out in a very concise but easy-to-follow manner. Will watch it a couple of times!
Thank you 😊
Wigner Eckart Theorem has frustrated me for quite a week how lucky was i be able too find such a video after six hours it posted
What a coincidence :P
I am working my way through grad school; yet this short video is the first time I learned what Wigner-Eckart theorem really means. Thanks a lot. You made my day :-)
We're glad to hear that, thanks for your comment! The Wigner-Eckart theorem was also something that confused us a bit, so we thought that's a great topic for a video!
I spent 4 hours trying to do an exercise of this, after this video I did it in 5 min. Thanks!
That's great!! Happy to hear this!
I was stucked about 3 days, it's hard for me without any example in the book. Thank you so much.
We‘re glad we could help :)
You just condensed a 90 minute lecture of ??? into the best AH-HAH! moment of my life. You are a genius, thanks so much :D
Thank you for your nice comment! That‘s exactly what we want to achieve with our videos! :D
I don't know how to thank you for your contents . Life savior
That‘s very kind, thank you! Just keep watching :D
Recently had my first exposure to the Wigner-Eckart theorem and was wondering about its uses in more detail, thanks for this great video!
Thanks for the nice feedback! :)
I love the motivation part of it. It helps me understand it easier.
That's great, thanks for the nice feedback!
While preparing some material for a course I'm teaching, I stumbled upon this beautiful channel and its clear and visual explanations. Really good stuff. Certainly gonna recommend it to my colleagues and students. Keep it up.
Thank you very much, this means a lot to us! :)
Mamma mia! Sei fantastico! Thank you for this wonderful video!
Grazie mille :D Thanks for watching!
Amazing video! made sense all the way through, which is a tough one
Thanks for the nice comment!
Thank you for making me understand this theorem. I use these for my PhD calculations... Your video helped me understand.. Cheers!!
Great work. Keep on going I will recommend your videos to other physics students. Greets from Technical University Graz in Austria :)
That's awesome, thank you very much! This really helps our channel grow 😊
Hare Krsna, this is awesome!
Thank you for the clean and straightforward presentation, and for adding a nice, simple example at the end, a real easter treat for me right now :)
Thank you for the kind words! :)
What a great video! Clear, easy, and to the point. Thanks!
Thank you very much! :)
Many thanks, from one prepairing the qualification exam of Ph.D.
Tomorrow is my exam and i am leaving it in the morning just to understand clearly with a fresh mind.😂not a backbencher but just like them ✌️
Bro, You saved my life, Ty
Awesome, thanks for watching :D
This is so funny because I just went over the C-G Theorem in quantum 3 but this is much more helpful.
Edit: ok actually I saw this in quantum 1, but it was nice too see it again in here.
Glad you liked the video! Thanks for sticking around!
Well I'm a physics major so why wouldn't I?
:D
Thanks really helped us out here
Awesome! Glad you found the video useful! 👍
This is gold, dude.
Thanks. Now I know what to use this for and have sample cases I can try out.
Be sure to check out the pinned comment where we corrected a mistake!
What a great video! Thank you!
Hello! in 1:00, you wrote |jm> as tensor product! But how can this be true? Since they(j,m) both live in a same hilbert space, tensor product seems to be just wrong. Also my professor told me that |jm> is not a tensor product between |j> & |m>..
Excellent work!
Thank you! Glad you liked it!
Thank you SO much for this!!! ❤️
:)
When solving the simplest case at 5:13 - where does the radial part of the electric field go? E = Ez = Ercos(\theta). Is all the radial dependence incorporated into the inner product for the ket state n=3?
Good question, we unfortunately made a mistake when calculating the integral, check out the pinned comment for more details! 🥲
Thanks for your video!
Can someone explain 6:10 - 6:16 to me please? Why ist it rank 1 and the 0 component?
z is part of a vector: (x,y,z). Therefore, the rank is 1, that's basically the definition of what a vector is. Next, in the spherical basis, you can write the position vector r like this:
r_+ = x + i y
r_0 = z
r_- = x - i y
Therefore, z is exactly the 0-component of the rank-1 tensor r!
@@PrettyMuchPhysics thank you!
@@Kerbaro You're welcome! For more information, we have a whole video on the spherical basis: th-cam.com/video/1XkZSl-1Mrc/w-d-xo.html
Hi,
Thank you a lot!
I was wondering about the radial part of function where you said its 1
should I calculate it for another state?
I asking that because you here said = 1
thanks again!!
Since \hat z = cos(theta) did not depend on r, there was no need to write the radial part of the wave function in its position basis in order to integrate it. If, however, the operator would have been r^2 (or something similar), we would have had to write |3> as and integrate over r.
But since every r-dependence was inside the |3>, we were able to make use of the orthogonality of R_n(r) and simply write = 1.
Hope this helps!
@@PrettyMuchPhysics I think you already know that you are amazing!!
millions of thanks!
You‘re too kind :)
@@PrettyMuchPhysics How is $E \hat z$ the relevant operator in this condition instead of $Ez$. Won't the latter tell us about the matrix elements of the perturbation? Let's say we are doing degenerate perturbation theory.
U are truly amazing😍😍😍
Thank you!
AT 5:21 why did you wrote E*z shouldn't it be E*zhat the unit vector
This matrix element is for instance important in calculating the Stark effect. There, you have an electric field, which leads to an additional potential in the Hamiltonian. This electric field generates a potential by coupling to the electric dipole moment, which is proportional to \vec r. Therefore, the product of E and r is interesting, which simplifies to E z if E only points in z-direction.
SO GREAT. Thank you so much
:D
Great video!
Thank you very much!
Great explanation. So in the same way I can find the transition probability induced by the dipole operator?
Yes!
Wonderful.
Thank you so much! :D
You are Genius thanks a million
That‘s very kind :) Thanks for watching!
WK Theorem has frustrated me for a couple weeks
How lucky was i be able to find this before midterm exam
We're glad you found to our video :D
Thank you very much!!! But is the subscript of C reversed at 6m24'
The index order does not really matter, but yes, unfortunately it‘s inconsistent with what we wrote in the top right corner. Thanks for letting us know!
Thank You
:) Thanks for watching!
I’m pretty new in this stuff so sorry if this is a silly question: how can you go from Y_10 to T_0^{1}? i.e. how can a function be equal to a tensor? I have learned that any Cartesian rank 2 tensor, say a 3x3 matrix, can be decomposed into irreducible representation basis (irreps) using rank-0,1,2 spherical tensors; are these tensors the same as those mentioned in this video ( T_q^k)? And how, please? Thanks a lot!🙏 🙏🙏
I am assuming you're referring to the part around 06:10.
It might be a bit sloppy, but the important thing is, that we start with an operator (z) and end with an operator (T^(1)_0). The part in the middle is there to show you that z indeed behaves like Y_10, and since the spherical harmonics are a basis, z can only be represented by a spherical tensor (T) with the same lm as Y_10. Therefore we identify z with (1)
beautiful
Thank you very much! :D
What software do you use? I've being teatching online but need a better whiteboard
We use an iPad app called Explain Everything!
Good Lord, why the books cant be as clear as you are. Thanks.
Thank you :D
Hi PMP! I want to calculate reduced matrix elements for H2 molecule using python......is ther any way to do so......
I have calculated wave function matrix for H2, can i use it to calculate reduced matrix elements.....
Within the scope of the Wigner-Eckart theorem, you get the reduced matrix element by doing a full calculation first, and then diving by the Clebsch-Gordan coefficient.
Your the top g
At the beginning you define z=rcos theta but when you apply the WE theorem you consider z=cos theta (without r). Why?
Good question, I don't know why we forgot about that, the "r" should be included 🙈 Fortunately, this only affects the numerical value at the end, so instead of 2/sqrt(15) you'd get some different number. Thanks for letting us know!
Damnn i finally understood it
That‘s great, glad you liked it!
Nice.
:D
wow
😬
thanks for saving my ass mate
Any time :D
you are the messiah
volume is low
Gordan =JORDAN. ????
Gordan = Gordan!