I don't quite understand what's happening at 16:45, what exactly does delta-ij mean? If it's an orthonormal basis, isn't every vector orthogonal to each other, so every inner product = 0 (ie: = 0)?
I think it's the fact that he's writing x,y,z as unit vectors that gives way for an orthonormal basis. Not every vector is orthogonal to each other, that's why we use the Kronecker delta to represent. Assuming the vectors are normalized, this function will "filter" xj's that are orthonormal to xi's, from my understanding at least. It's very reminiscent of Fourier transforms, however we just started learning that in class so not sure how much help I can provide there. I'm pretty new to this subject so please correct me if I've made any errors! Cheers.
@@edubski3608 I'll be honest, I understood very little of what you said but that's because I am pretty new to this myself. And I don't know what's a "Kronecker delta." I guess I have a long way to go but I did understand most of the video, so I think he's a really good teacher lol. But thanks for your help!
@@akashagnihotri2469 If you're trying to learn this subject, this series in particular follows the first three chapters from Griffiths' Intro To Quantum Mechanics, I would highly recommend you pick up a copy (2nd or 3rd edition, whichever is cheaper) used. As far as learning more about vector orthogonality, doing more research on inner products in particular along with fourier transforms, should provide you with some more background. Keep at it!
@@turboleggy I don't think I'm 100% sure on what you're asking, however it is correct to assume the inner product of x1 and x1 would be 1. You're basically asking how much of x1's state coincides with x1's state, which as we know, should be all of it.
Yo bless this prof he's singlehandedly saving my grades
I couldn't help but believe that I was learning math with Topher Grace.
I was just watching this video (again) and realized I've already watched it... because my dude here sounds like Topher Grace.
if this is intro then what is inside? O.o
Please confirm if answers for "Check your understanding" are 50 and 66
Yes
yes you are correct
you are right
How did you get 66?
For Check Your Understanding, did anyone else get 26 and 66?
Edit: Muddassir has it correct, it is 50 and 66. Work listed in comment below.
50 and 66
26 and 66
@@muddassirghoorun4322 40 and 66
I don't quite understand what's happening at 16:45, what exactly does delta-ij mean? If it's an orthonormal basis, isn't every vector orthogonal to each other, so every inner product = 0 (ie: = 0)?
I think it's the fact that he's writing x,y,z as unit vectors that gives way for an orthonormal basis. Not every vector is orthogonal to each other, that's why we use the Kronecker delta to represent. Assuming the vectors are normalized, this function will "filter" xj's that are orthonormal to xi's, from my understanding at least. It's very reminiscent of Fourier transforms, however we just started learning that in class so not sure how much help I can provide there. I'm pretty new to this subject so please correct me if I've made any errors! Cheers.
@@edubski3608 I'll be honest, I understood very little of what you said but that's because I am pretty new to this myself. And I don't know what's a "Kronecker delta." I guess I have a long way to go but I did understand most of the video, so I think he's a really good teacher lol. But thanks for your help!
@@akashagnihotri2469 If you're trying to learn this subject, this series in particular follows the first three chapters from Griffiths' Intro To Quantum Mechanics, I would highly recommend you pick up a copy (2nd or 3rd edition, whichever is cheaper) used. As far as learning more about vector orthogonality, doing more research on inner products in particular along with fourier transforms, should provide you with some more background. Keep at it!
What if both the vectors are x1? A vector is not orthogonal to itself. We are othronomal basis so =1.
@@turboleggy I don't think I'm 100% sure on what you're asking, however it is correct to assume the inner product of x1 and x1 would be 1. You're basically asking how much of x1's state coincides with x1's state, which as we know, should be all of it.