Commutators and Eigenvalues/Eigenvectors of Operators
ฝัง
- เผยแพร่เมื่อ 17 พ.ย. 2017
- In this video, I introduce the concept of commutators and eigenvalues/eigenvectors in Quantum Mechanics. After stating some properties (my apologies for inundating you with a bunch of statements), I then move on to discussing the 2nd Postulate of Quantum Mechanics.
This should all be a nice build-up to the video where I finally prove the Generalized Uncertainty Principle!
Questions? Ask in the comments!
Prereqs: The videos in my Quantum Mechanics playlist before this one - • Quantum Mechanics: Mat...
Lecture Notes: drive.google.com/open?id=1CKK...
Patreon: www.patreon.com/user?u=4354534
Twitter: FacultyOfKhan?lan...
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- Jennifer Helfman
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wow this always seemed so complicated to me. Ur explanations were very concise n to the point :)
Glad to help!
Excellent summary. Looking forward to the uncertainty principle (hopefully more discussion on compatible observables?).
Would also like to see ones on the correspondence principle & The Ehrenfest theorem (perhaps after you've covered time dependence?).
Please dont stop. I am learnig new complex thing. Thank you. By the way you deserve more follower but this topics are very high to many people
Amazing job on presentation and explanation. Everything is well organized, clear, and broken down with the quality off the roof. Thank you for making this series!
Thanks for this amazing video. I a studying QM and coming from a math background I get pretty amazed at how many different math concepts are involved. It is nice to go over this video series that goes over all the math concepts involved in a fairly short amount of time.
On a side note, I wonder where the jacobi identity for commutators is used in QM.
The best so far, it's unique of its kind. Keep going
Thank u for your effort bro, wish u a good luck
I can't thank you enough you're amazing
beautiful explanation! Thumbs up.
Thank you!
Hi, As usual, your lectures are nice. Buy I think that the 4 property of opperators shows that B produces a subspace of the space of A operator. What do u think?
excellent sir please upload more videos about commutator problems
The specific form of the operators (position and momentum in this case) depends on the basis you choose. The example in the video is in the position basis. 😃
Shouldn' t the momentum operator (at least in position representation) be - i hbar times partial derivate? Why do you write it as hbar/i ?
Because of the anti-symmetry and Jacobi identity, that means that the commutator is a Lie Bracket correct?
Is Lie bracket the same as commutator ?
Are measurable quantities real life estimates like blood pressure, height….etc
How can you say that an operator commute with a scalar? Do you mean the scalar multiplied by the identity operator?
I know you stipulate a certain donation level on patreon to recommend videos, but I would love a formal break down of the Poisson bracket in use with the classical Hamiltonian to define the equations of motion. Like if you could work through an example from parametrizing coordinates and defining the Hamiltonian to finding the equations of motion, that would be much appreciated.
That donation level is only if you want videos in the next 2 weeks. I'll still take requests regardless (though I might get to them later)! In your case, I'll put it on my to-do list :)
Thank you chap!
I’m doing eigenvalues and eigenfunctions (PDE). Darn!
Interesting. I kind of touched on eigenvalues/eigenfunctions in my Sturm-Liouville video and my Eigenfunction Expansion (PDE) video. But is that something you would like to see me do?
Faculty of Khan Thanks! I will check out your S-L video.
What is Eigenstate
It's a state of a quantummechanical system for a particular operator. For example, when the energy-operator works on (a wavefunction describing) an electron in a hydrogen-atom it produces specific energystates (remember the shells electrons can be in?). These specific states are eigenstates for that the energy-operator. The position- and momentum-operator have their own eigenstates (depending on the system).
You are an UnderGrad Student ?
please eplain the property of completness
I've explained it in my Hilbert space video (4:15 for the relevant timestamp):
th-cam.com/video/7zx3MT9FgT0/w-d-xo.html
Sacripant de pub de Lancôme au milieu d’un explication, otherwise very cool video 😎
Actually, the eigenvalue lambda is a real number, not a complex number. Yes? Oh that is only true if the operator is Hermitian.
For specific operators (e.g. Hermitian operators, which is one of the more famous QM operator types), the eigenvalue is real, but in general, it's complex. Hope that helps!
Also, are you actually Estelle Asmodelle? I'm just curious because I didn't expect a well-known scientific writer to be hanging around on my channel, let alone TH-cam.
Yes, I am her. Brushing up on my QM maths for my PhD. This is review for me and your lectures are actually quite succinct !
Glad I can help! Good luck on your thesis!
Thanks, and keep the good work going.
😪😪 looks like rocket science
I guess it's exaggerating..
Oh really
He isn't teaching at all. He is just reading out from some book or notes. Disappointed by such approach. Definitely pressed dislike button.
Given an operator 𝐴
̂ = (𝑥
̂
𝑑
𝑑𝑥
+ 2). Calculate
(a) [𝐴
̂, 𝑥
(b)
̂]
[𝐴
̂,
𝑑
𝑑𝑥
]
. Some help