Ever heard of Quantum Operators and Commutators? (Explained for Beginners)!
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- Опубліковано 29 чер 2024
- What is a quantum operator? And just how useful are quantum commutators? Find out how they help us understand the Ehrenfest Theorem!
Hi everyone, I'm back with a new video! This time it's the first in a two-part mini-series on one of the coolest theorems in quantum mechanics - Ehrenfest's Theorem. With a good grasp of high school level mathematics, I believe it is possible to understand this theorem on a basic level. However, we need to do some groundwork first.
(Check out part 2 of this mini series here: • Quantum Physics Become... )
A quantum operator is a mathematical object / entity that corresponds to taking a measurement on a quantum system in real life. Examples of quantum operators include the position operator, the momentum operator, and the Hamiltonian operator. The Hamiltonian is an extremely important operator in quantum mechanics, consisting of kinetic energy and potential energy terms. It's also worth knowing that the operators we will deal with in this video are known as "observables". Entities that respond to things we can observe in the real world (such as position and momentum).
But one of the most interesting takeaways here is that in quantum mechanics, making a measurement is a complicated process. Unlike in classical physics, making a measurement doesn't necessarily affect or alter the system in some way, quantum mechanics tells us that a measurement fundamentally changes the wave function of the system. This process (of taking a measurement, causing the wave function to change) is known as the "collapse of the wave function". And mathematically, this process of making a measurement is represented by "applying" a quantum operator to the wave function ket of a system. The wave function, remember, is just a mathematical representation of all the information we have about our system. It is directly related to the probability distribution of the system, meaning it tells us the likelihood of finding particles that part of our system, in different locations in space (and much more).
Now, because measurements are fundamentally system-altering in quantum mechanics, this means that the order in which we make two measurements can actually give us different results. For example, if we were to measure a quantum system's position, and then its momentum, we might get different results to if we measured its momentum first, and then its position. For this reason, it becomes useful to define a mathematical quantity known as the "commutator" between two measurement operators.
A commutator is just a measure of the difference in results when we measure one quantity (e.g. position) and then the other (e.g. momentum), as compared to when we measure them the other way round (i.e. momentum first, and then position). If switching the order gives us different results, then the commutator is not zero, and the order in which we make measurements needs to be considered carefully. However, in some cases the order does not matter. For such cases (and such pairs of operators), the commutator is zero. This is similar to saying 2 x 5 = 5 x 2. Multiplication is a commutative operation, meaning the order in which we multiply the two numbers does not matter.
Once we learn enough about operators and commutators, we can start to notice that they show up in Ehrenfest's theorem! In the finale of this two-part mini-series, we will be learning about expectation values (very important to QM) and then finally putting it all together to understand what Ehrenfest's Theorem is trying to tell us.
If you enjoyed this video, please do hit the thumbs up and subscribe for more fun physics content. Feel free to hit the bell button to be notified every time I upload. Check out my second channel, "Parth G's Shenanigans" for some music, and follow me on Instagram @parthvlogs to see what I get up to on a more day-to-day basis. Thanks for watching, I'll see you soon!
Hi friends! Part 2 of this series is out now! Check it out on my channel, or down below!
Hi friends, check it out here: ua-cam.com/video/dHptQCXdQio/v-deo.html
Sure. Great explanation! I ALWAYS WANTED TO KNOW THE MEANING OF EHRENFEST'S THEOREM. Thanks!
Awesome work! Subscribed now!
check out quantum physics Professor Basil J. Hiley on how the operators are fundamental instead of just "acting on" the wave function. Noncommutativity is the key to nonlocality. Maybe if Ehrenfest had known this he wouldn't have committed suicide.
My High Sch Math Knowledge + My interest towards Quantum Mechanics = This video is awsm
same!!!!!
How old are you?
@@kanhapanday6754 when this video was made, I was 17 - 12th standard. Now I'm 19, pursuing UG in physics 2nd year
I was really willing to learn quantum operators. Thanks Parth for making this 😁😁
Thanks for watching :D
@@ParthGChannel I just really love all your videos 🤗🤗
Can’t wait to see part 2
I used laugh being indian when foreign people used say that everything becomes easy when an indian teaches you. After watching your videos I believe they were right.
Damn True Man !!!
Only if you can't understand them. This guy here speaks good English but most of them are terrible.
Just love the way you explain difficult things. Your work is really appreciable. Thank you so much.
These videos are really well done. I am a retired engineer that always loved physics so I have spent a lot of time reading and studying since I wrapped up work.
I'm amazed at this subject and the facility with which you explain it! I would also like you to give a physical interpretation of what it means for operators to commute. Keep it up and greetings from Colombia!
Wish I knew about your channel earlier... Love how you explain QM. I'm officially a fan.
Very nice presentation on commutators, Parth. You explained the value of knowing how this applies in QM problems.
Very interesting, informative and worthwhile video. To say this video is excellent is an understatement; this video, and others by Parth are absolutely superb and a must see for anyone interested in the sciences.
I have a hard time understanding this operators, but when you explain it, I now have a better understanding of it.
Oh my god!!!!
1- your voice is calm and relaxing
2- you explain things smoothly
3- i JUST realized the physical meaning of commutation and the operator order things from YOU and i screamed! Mind blow!!
4- you sum up the video at the end, this shows you really *care* that viewers really *understand*!
I subscribed at one point when i was watching the video, then THREE times during it i thought of subscribing before realizing that i already did.
Sir, thank you!
You are doing a great job bringing these advanced notations to common people interested to explore the front shores of science. 👍
Watching this as a graduate doing a masters in physics. This is a really good description and explanation for approaching this topic of learning. Good work mate
A hundred "Likes". You are the first I've seen to give an intuitive conceptual explanation of commutators before giving the definition. Perfect!
I am in love with his way of teaching.he makes everything so easy to understand.. amazing
Really well explained
You do it better ;)
Hi, I just wanted to say thank you so much! I am an undergraduate physics major and have my quantum physics exam in two weeks. This helped me so much! I was really confused after the lecture, but now I think I start to understand the topic. I wish you were my profesor...
Wow I've been watching some of your videos and it's basically impossible NOT to understand.. best QM videos on YT to me, thank you!
Thanks Parth these videos doing bits for my revision - year 2 uni physics
You make QP really friendly, thank you for sharing Parth
Great video, my QM lecturer sucked at explaining commutators so this was very much appreciated!
I can totally relate... Either that or I just wasn't listening 😅
same same... most university professors are shit in quantum
Brilliant explanation, thank you Parth!
Parth you are really making quantum mechanics interesting.... waiting for your next video brother
For first time in my life I actually understood a concept of Quantum Mechanics. Tysm
This video is a pretty good video, and in general this channel provides something I think is missing from a lot of book, an explanation of what the physics is. I’ve read about commutators, but never understood why they were important until now.
Actually fun physics without the sugar coating! Awesome work !!!
Thank you for this ! I’m a middle schooler with a passion for math and this was explained so well I can even understand it
Beautiful! Thank you.
Really well explained professor at my university was not even able to make us understand about this simple thing. Really thanks for this informative video
u r COOOOOOOOL, brother. im just a highschool student who is generally not much good at math but i was still able to grasp the things that u mentioned.
I’m an undergraduate student and currently studying in this topic. This video is very helpful. Thanks a million. :)
what a good video with a really good explanation !!
thank you. will be waiting for part 2.
*Thanks for this, this was really helpful*
Nice video ... Very well explained
Awesome video,I understood everything Parth, I've a small request,can you make a small series on basics of physics...like everything which a new,basic student can understand...pls, I'll be happy if you'll take that initiative✌️💯
Damn, I haven't been this early in ages. Great stuff mate, looking forward to more from you!
Thanks very much! :D
Great and understandable explanation, thanks!
Thanks! great explanation!
That's perfect. Wish you all the best.
hello Sir!,i just want to thank you for really clear explanations and also a person can easily recognize that you have understood physics subjects really well (:
Thank you for your expertise and information. What you give to non physics people like me is invaluable.
Smooth introduction to why commutators are so useful, very nice :D
Awesome video can't wait to see the next video thanks👍👍
Thanks very much :D
Awesome explanation mate
very well done, thank you
Well,thank you so much first of all for making it so easy
looking forward for the next video 👍
Waiting patiently for part 2 of this ;)
Around 5:30-5:44, there’s an error. Probability is proportional to | psi |^2 not (psi)^2. This is extremely crucial as wavefunction is in general complex and (psi)^2 yields a complex number and we cannot “measure” complex numbers. We need the solution in terms of real numbers hence the modulus is important.
yeah that's right. But we mainly focus on the commutators in the video, so we can ignore this little thing. But yes, thanks for pointing out the error.
Great Explanation 👍
Was waiting for your videos
I do not comment often , but I should tell u that u r doing a great job , and thank you for saving me today , hug from Vienna
This is an invaluable video as a physics hons undergrad
Your videos are amazing Parth....... X
Extraaaaaaordinary ....awaiting the next
It's really amazing 👏👏
Great work.
ur videos r extreemly good :) thanks
Thanks to make it that easy !!
Operators +×÷- are high school mathematics. Operators in quantum mechanics are extensions of the above operators (comprehensible to every day life), which are not comprehensible to every day life but needed to do calculations in a different kind of mechanics known as quantum mechanics
thanks brother , this viedo is beautiful understanding for me .
again thank you
Great Video!!
Excellent video!
I do not know if you can make a video explaining CPT Symmetry, I tried to read about that but I am still lost in some concepts
Thanks for your videos!
Who are you bro? So much passion to make us learn with extreme quality. Hope one day I will become like you. Very informative video and thanks for the video. Will always be supporting you......- big fan
You are a great teacher. Could you please make a video about the alcoubierre drive? That would be really nice.
This was useful
Thanks
It was a great video.. will you plaease make one explaining CSCO.. thnak you
Very clear
Hey Parth.. nice content of scientific context in a way simple terms... Two things peculiar about this:
1) why strangely is the commuter result of position and momentum have a complex value to it when what u measure are basically two real quantities
2) in regards to consious argument it's more like the single electron slit experiment where diffraction pattern isn't observed just because some weird way the electron knows we are measuring it.. but in double slit experiment even when we have a observer(detector) in one slit even though the likely is 50-50 it's more like the electron passes through other slit.. so the whole picture of electron knowing that we are measuring it influences the particle nature
Thank you very much
Fabulous, ab to mai aap hi se QM padhunga bhaiya!!! Mai aur kuch nhi jaanta!!!
Could you make an explanation video for the standard model of quantum mechanics, pls ?
I really would like to know about quarks and leptons, as well as the force carrier particles.
Seriously, I enjoy watching your videos as I like the way you explain things simply.
Worth watching
Thanks Partha g dada..🙏
Classy content
I don't know if you will see this but I was struggling recently in my senior year with all the notation and was worried about whether I'd make it in this class. Your succinct explanations have opened my eyes and made me realize things in a way where I no longer see babble but see actual logic behind what I am reading. Thanks so much, you're amazing!
If you are struggling with notation, then you shouldn't be in the field. This is absolutely trivial shit, kid. ;-)
@@schmetterling4477 why do u say that TvT
@@silverspin Why do I say what? That one has to know what a scalar product is and how linear operators work? Because that's the math that's in play here. If you want to read Homer in its original language then you better learn classic Greek. ;-)
Thank you sir
thank you !
Excellent
very good video
Literally i was waiting for ur video before going sleeping 😂
Btw love ur videos ❤️❤️🇮🇳
Hi
Hello
Yea give me some love too. Indian here
THANK YOU
Thanks buddy 😊
Thank you
I think, if we can use classical physics. We can see that Ek = 1/2mv^2. And momentum is p = m*v. If we multiply kinetic energy by m/m (which is basically as same as multiplying by one), we get Ek = (m^2*v^2)/(2*m). And we can see that we can write this as Ek = (p^2)/2m.
:))
Nice video Parth
Thanks a ton...
Very good
Nice video sir
mini little series..hmmm...guess u can call them quantum series. loved the video btw :)
Nice cliffhanger!
Best youtube chanel
Yes get in, Parth is back!
Just an observation, the operator applied to the wave function looks similar to an argument applied to a function (mathematical or as in a program), from which we get a value.
Amazing 🔥🤘🔥🤘🔥🤘
Please make video on some high level calculus used it physics like partial derivative , etc...
Btw lots of love from india❤️❤️
Khan Academy has very good videos on multivariate calculus. You should go check that out :)
thx for this video :))))
Bhaiyaa
You know what, i m a 10th grade student bt am still able to understand ur videos on such high level topics to a large extent (though i forget them very soon😂) bt still thankyou🙂
Parth can you please make a video on particle in a box model in quantum mechanics