Orbital angular momentum in quantum mechanics

[@srushtipatil9351]

Why didn’t I find this channel earlier!!this is gem✨

[@ProfessorMdoesScience]

Glad you've found it now! :-)

[@Toro00_g9]

Me too

[@impulse894]

Best and easiest explanation! Also, you are very precise even in notation and intervals which we appreciate. No playing around, just some old school rigorous physics! 🖤

[@ProfessorMdoesScience]

Thanks for watching, and glad you like it!

[@devrajbahl]

despite few subscribers, your content is great

[@ProfessorMdoesScience]

Thanks for your support, and do tell your friends! :)

[@michelecasazza2864]

Most clear explaination i ever got, thank you for your videos, please keep at it, you are great!

[@ProfessorMdoesScience]

Thanks for watching and for your support! :)

[@luckymishra6056]

Very nice explanation thanku so much . Where are you from ma'am ????

[@ProfessorMdoesScience]

I work at the University of Cambridge in the UK :)

[@houhoutrad8748]

You are really doing a GREAT JOB Professor M team, I really wish you the best

[@ProfessorMdoesScience]

Thank you very much!!

[@shahdmehmood1288]

Thank You So Much Professor M Does Sicence for this Helping Materials. God Bless You for a lot of Blessings.

[@ProfessorMdoesScience]

Glad you like our videos! :)

[@richardthomas3577]

Nice, as always! Even in areas I already know, your videos are so clean and crisp they really help. Thank you! BTW, the differing theta/phi conventions in math and physics are mildly annoying -- don't you wish people would just agree on conventions very early on? (There can be a lot of value in different notations -- thank you Mr. Feynman! -- but it is hard to see the value in different conventions like this.)

[@ProfessorMdoesScience]

Thanks for your kind words! And totally agree that differing conventions are midly annoying, but unfortunately we have to live with them...

[@sofiallacer5951]

Super good explanation!!

[@ProfessorMdoesScience]

Glad you like it! :)

[@ayushdhingra855]

Your channel help lot in QM.... Thank you so much 😊

[@ProfessorMdoesScience]

Glad to be of help!

[@workerpowernow]

very clear derivation. Thank you

[@ProfessorMdoesScience]

Glad you found it clear! :)

[@pete4043]

this channel is way better than the indian channels

[@ProfessorMdoesScience]

Glad you like our videos!

[@muhammadahmad4610]

Good Work, which software is used for making videos

[@ProfessorMdoesScience]

We use Explain Everything to make the videos

[@nishitchaudhary9455]

Amazing...... 💥

[@ProfessorMdoesScience]

Thanks! :)

[@hesokaheso855]

holy crap i found a gem in the clutter of wool. *Subscribes*

[@ProfessorMdoesScience]

Thanks!! :)

[@Fatemehsoltani16]

That was perfect 😇❤️ milion thanks for your time

[@ProfessorMdoesScience]

Glad you liked it!

[@andreapaolino5905]

I was trying to derive the identities at the end of the video for the L+ and L- operators, and I've stumbled upon the following question: how come when I derive them from the definition they indeed come out equal to the ones shown in the video, but when I derive one from the either (let's say L- from L+) via complex conjugation/hermitian conjugation I get a sign error? Specifically, if I apply such conjugation to L+ (hoping to get L-) I actually end up with h_bar e^(-i phi) (d/dtheta - i/tan theta d/d phi), which doesn't match the result by a factor of minus -1. Am I missing something here (like a trivial trig identity) or am I just abusing complex conjugation in the wrong way? Any help/tip/advice would be greatly appreciated, thanks as always for the awesome content

[@ProfessorMdoesScience]

In general you should get the correct expression. Without seeing more details of your derivation it is hard to identify where the error/confusion arises. But you should get the same answer, so I would encourage you to try again!

[@Imran52Feb]

What are L plus and L Minus operators? Rest I understood. Thanks Professor madam.

[@justgivemethetruth]

If you have a solid uniform sphere where a ray projected from the center of the sphere through a point on the surface points fixedly to a certain star at infinite distance in space ... that is, the sphere is not rotating relative to the fixed stars, and that sphere is out in deep space approaching the Earth - to be eventually captured by the earth into an orbit; then as that sphere goes into orbit, and then orbits around the Earth does that ray projected from the center of the sphere through the point on its surface stay pointed in one direction or does it rotate in some way different from how it did when it was not orbiting the Earth?

[@ProfessorMdoesScience]

This is an interesting question, although it is about classical rather than quantum mechanics. We may cover this sometime in the future!

[@justgivemethetruth]

@@ProfessorMdoesScience I can't see any force that imparts rotation to the sphere, but if it doesn't rotate relative to the stars, it must have a relative rotation as it circles the Earth ... right, because it would be rotating once per orbit ? Of course then it would also be in a weird orbit around the sun too. Kind of makes me dizzy to think about.

[@ProfessorMdoesScience]

I recommend you look up "rigid body mechanics" to understand this problem. This area of classical mechanics describes the motion of extended bodies (like your sphere) under the action of external forces (like the gravitational force exerted by Earth).

[@justgivemethetruth]

@@ProfessorMdoesScience Thanks for the recommendation, but I've had university physics and I don't think i am going to figure this out with any level of confidence. I'm wondering that since the moon has the same face towards the Earth at all times, that would seem to indicate that it is fixed angular momentum relative to the sun, but not necessarily the fixed stars. I was hoping for a pointer to someone that might have referenced this problem before. Every time I think about this it perplexes me.

[@ernek89]

Thank you, It would be great if this could be explained in another video in matrix formulation to compute L eigenvalues for an example of an atomic system in AO basis , I.e an electron in a p órbital. Any resources that you could recommend on this particular aspect? Amazing job!!!

[@ProfessorMdoesScience]

Thanks for watching! We're preparing a series of videos on the hydrogen atom, which should serve as a stepping stone towards more complex atomic systems. Thanks for the suggestion!

[@afaq7564]

Brilliant Explaination madam😍

[@ProfessorMdoesScience]

Glad you liked it!

[@subhajitsadhukhan8521]

What about the videos on spin angular momentum? When will they come? 🙂

[@ProfessorMdoesScience]

Already responded to your other question, but for completeness: we are currently working on videos covering the hydrogen atom, and after that we should move to spin.

[@DrMarcoArmenta]

I'm a little bit confused... I think I've never seen the definition of the operators x,y,z or px,py,pz. These should be matrices right? how are they defined?

[@ProfessorMdoesScience]

One could in principle represent these operators as matrices, but in practice that wouldn't be very convenient because they describe continuous variables. It is easiest to understand these operators in the so-called position representation, and we explore them in this series of videos, which should be a good starting point: kzbin.info/aero/PL8W2boV7eVfnHHCwSB7Y0jtvyWkN49UaZ I hope this helps!

[@shakiralsaidi5437]

thank you

[@ProfessorMdoesScience]

Thanks for watching!

[@Professional_chemist]

Amazing! Thank u :)

[@ProfessorMdoesScience]

Thanks for watching! :)

[@افهمأكثر-ز8ك]

شكرا جزيلا على التوضيح. اسأل الله ان يوفقكي في حياتكي

[@zaphantom3181]

Confused. d(theta)/dz 's value is different from the textbook. I got -1/rsin(theta) instead of -1sin(theta)/r.

[@ProfessorMdoesScience]

What point of the video are you exactly referring to? I am not sure I find an explicitly calculated d(theta)/dz.

[@devrajbahl]

I'm a high school student thus only came for formula but I pretty much understand all of it.i wonder why?

[@ProfessorMdoesScience]

This topic is typically taught at the undergraduate university level, so it is great that you can understand it!

[@ajilbabu13]

If we dont have any classical background for formulating the algbra of L(or any orher observable), will we able to derive this?

[@ProfessorMdoesScience]

An example of what you are asking is what happens with spin: there is no classical version of it. Historically, there were a number of experimental results (e.g. Stern-Gerlach) that couldn't be explained without the introduction of a new quantity (spin). I guess ingenuity plays a big role in figuring out the relevant algebra there...

[@devrajbahl]

I wonder where you work at?

[@ProfessorMdoesScience]

We are both academics at the University of Cambridge.

[@praveenkumarmorabad1358]

Thank you madam 🙏

[@ProfessorMdoesScience]

Thank you for watching!

[@snjy1619]

[@dilshodkhodjayev8486]

Amazing, but you do realize some of us not so great at understanding formulas, would be nice if you at least give a hint how did you derived the terms instead of just voicing them

[@ProfessorMdoesScience]

Thanks for the feedback, could you please specify which steps are unclear?

[@amaljeevk3950]

❤

[@daminisahu7469]

❤

[@HernandezOmarCharlie]

L