at 51:22 , why do we not consider another set of states labelled by negative j. Maybe these positive and negative j states have the same eigenvalue for J^2 but might behave differently, under the action of perhaps another operator. Could someone please explain, why that possibility is ruled out ?
i saw his lecture note on OCW website and it said that "we can simply use j>=0. And you should not think that there are two different states with two different j's associated with the eigenvalue hj(j+1).It is just one state that we are labeling in an unusual way. Of course, a theory may end up having more than one state with the same J^2 eigenvalue but in that case we will have more than one state with the same j>0."
At 1:11:48 after working out the possible values of j, how does he immediately relate this to the spin of the particle? We have previously not defined j as anything but the eigenvalue of some J^2 operator right?
j here is a general label for angular momentum. it can be either spin or orbital ! What is it will completely depend on the system we are discussing and nothing else. the algebra of j holds for both L and S.
A two dimensional harmonic oscillator can move on a circle. Why shouldn't it produce an angular momentum around the z axis? And if you define ax +/- ay, then you exactly have the phase shift of pi/2 to make it happen, as you need sin and cos.
ONCE AGAIN, mr Zwiebach is very interested in the mathematical side of QM. But what about the physical side? According to QM, angular momentum L = (l . (l + 1))^2, with the quantum number l = n - 1. So when n = 1 = the ground state, we have l = 0. But l = 0 results in no angular momentum L !!! This means that in its ground state, the H-atom has an electron that isn't revolving around the nucleus. Ask mr Zwiebach how he explains this. Because in the entire course, he won't tell you about this physical problem.
No, it's correct. You may have found that the radial part of the Laplacian is (1/r^2)*(d/dr)(r^2d/dr) which looks different but it's equivalent to the radial part presented in the lecture. You can check the action of both operators on some arbitrary function and see they are the same operator.
Pure Gobbledygook( Yes, that is an actual word- you can look it up). It is obvious that this mathematical language ( believe me, if you take the time to transcribe the actual words from the mouth of Professor Zweibach's mouth, and not the equations of symbols he writes), you will have nothing but pure Gobbledygook, if you step back and READ his words, and don't look at his symbols on the blackboard. The examination of the universe taken all the way to the sub atomic particle level, by mortal fallible men, driven by the mindset/belief/faith, in the atheistic THEORY of evolution, and over centuries, has produced these Gobbledygook THEORIES. And for what? Step back and just look at how the world of mankind(cosmos), and the actual literal world( terra firma), is just becoming more and more harmonious and beautiful all the time. There are no problems confronting mankind or the earth at all!!! No violence, no pollution, no extinct species, no climate change, no wars, no homelessness, no starvation, no problems at all!!! Science and atheistic Theories that exclude intelligent design and a creator, have produced all this gobbledygook language and it's harmonious end results of a much better, no problem, carefree, and loving world of peace and tranquility. OH!!??? It hasn't done that?? Get off the fallible manmade treadmill of atheistic THEORY that produces nothing more than gobbledygook, chaos, and non harmonious negativity. I come here to listen and fall asleep. This works as great asmr for me. All the chalk writing on the blackboard sends me to blissful sleep. That's all that theoretical gobbledygook does for me. Paying strict attention to all this is only good so as to get a passing grade in this course. It is a mathematical and atheistic view of the world. Men thinking that the physical universe can be truly defined and understood, even to the particle level, is actually funny and sad at the same time. Creating equations to completely explain EVERYTHING in the created designed universe, is only possible and and endeavor( if chosen) by the Almighty creator. Not by the creation. Man can only create suppositions and theories. He has done this in massive abundance. Look at the world around you. This is what theories of fallible men produce. The world of today. On the brink of extinction. Pure Gobbledygook.
I love this Professor! He's amazing!
Absolutely! After his watching lectures on QM, it feels like another level.
at 51:22 , why do we not consider another set of states labelled by negative j. Maybe these positive and negative j states have the same eigenvalue for J^2 but might behave differently, under the action of perhaps another operator. Could someone please explain, why that possibility is ruled out ?
i saw his lecture note on OCW website and it said that "we can simply use j>=0. And you should not think that there are two different states with two different j's associated with the eigenvalue hj(j+1).It is just one state that we are labeling in an unusual way. Of course, a theory may end up having more than one state with the same J^2 eigenvalue but in that case we will have more than one state with the same j>0."
At 1:11:48 after working out the possible values of j, how does he immediately relate this to the spin of the particle? We have previously not defined j as anything but the eigenvalue of some J^2 operator right?
j here is a general label for angular momentum. it can be either spin or orbital !
What is it will completely depend on the system we are discussing and nothing else. the algebra of j holds for both L and S.
For the first time in about 40 lessons of prof. Zwiebach, I get lost!
CC fixes:
21:15 unit sphere
41:08 adjoints of each other
41:33 increase the Z component
57:10 the adjoint
Done
all this talk about Jay z and he doesn't even mention beyonce...#rude
lmao glad im not the only one thinking this
is this brainrot 9 years ago?
A two dimensional harmonic oscillator can move on a circle. Why shouldn't it produce an angular momentum around the z axis? And if you define ax +/- ay, then you exactly have the phase shift of pi/2 to make it happen, as you need sin and cos.
ONCE AGAIN, mr Zwiebach is very interested in the mathematical side of QM. But what about the physical side? According to QM, angular momentum L = (l . (l + 1))^2, with the quantum number l = n - 1. So when n = 1 = the ground state, we have l = 0. But l = 0 results in no angular momentum L !!! This means that in its ground state, the H-atom has an electron that isn't revolving around the nucleus. Ask mr Zwiebach how he explains this. Because in the entire course, he won't tell you about this physical problem.
38:39 - drawing on table
38:39 - drawing on table
awesome professor
38:39 - drawing on table
Laplacian of spherical co-ordinate is wrong or correct me .
No, it's correct.
You may have found that the radial part of the Laplacian is (1/r^2)*(d/dr)(r^2d/dr) which looks different but it's equivalent to the radial part presented in the lecture.
You can check the action of both operators on some arbitrary function and see they are the same operator.
Has he discussed the 2D SHO in a previous lecture?
It was done in a homework problem set. We analyzed it in the homework.
Thanks ❤️🤍
loving it
A little discussion of may be 5 6 lectures
Thanks Prof!
Jz, real gang. #StayTrue
Best video ✌
Jay Z really!!! Lol
Pure Gobbledygook( Yes, that is an actual word- you can look it up). It is obvious that this mathematical language ( believe me, if you take the time to transcribe the actual words from the mouth of Professor Zweibach's mouth, and not the equations of symbols he writes), you will have nothing but pure Gobbledygook, if you step back and READ his words, and don't look at his symbols on the blackboard. The examination of the universe taken all the way to the sub atomic particle level, by mortal fallible men, driven by the mindset/belief/faith, in the atheistic THEORY of evolution, and over centuries, has produced these Gobbledygook THEORIES. And for what? Step back and just look at how the world of mankind(cosmos), and the actual literal world( terra firma), is just becoming more and more harmonious and beautiful all the time. There are no problems confronting mankind or the earth at all!!! No violence, no pollution, no extinct species, no climate change, no wars, no homelessness, no starvation, no problems at all!!! Science and atheistic Theories that exclude intelligent design and a creator, have produced all this gobbledygook language and it's harmonious end results of a much better, no problem, carefree, and loving world of peace and tranquility. OH!!??? It hasn't done that?? Get off the fallible manmade treadmill of atheistic THEORY that produces nothing more than gobbledygook, chaos, and non harmonious negativity.
I come here to listen and fall asleep. This works as great asmr for me. All the chalk writing on the blackboard sends me to blissful sleep. That's all that theoretical gobbledygook does for me. Paying strict attention to all this is only good so as to get a passing grade in this course. It is a mathematical and atheistic view of the world. Men thinking that the physical universe can be truly defined and understood, even to the particle level, is actually funny and sad at the same time. Creating equations to completely explain EVERYTHING in the created designed universe, is only possible and and endeavor( if chosen) by the Almighty creator. Not by the creation. Man can only create suppositions and theories. He has done this in massive abundance. Look at the world around you. This is what theories of fallible men produce. The world of today. On the brink of extinction. Pure Gobbledygook.
Thanks Prof!
Thanks Prof!