Position and Momentum Operators in Quantum Mechanics
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Күн бұрынWe've learned a bit about quantum mechanics from a strictly conceptual and qualitative standpoint. But now it's time to dig a little deeper. Quantum mechanics is mathematics, so if we want to understand it on a fundamental level, we have to dig into the math. Unfortunately, the math is rather complex, so a solid understanding of linear algebra and differential equations is assumed here. But luckily, I have covered all of these topics in my mathematics playlist, so if you are committed to understanding quantum mechanics but don't have the math background, just head over there first to get the math down, and then this stuff will make sense! In this video, we start out by learning about operators, what they are and how to use them, the position and momentum operators, and how to apply them to the wavefunction. Don't be scared, it's fun!
Script by Hèctor Mas
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@adamdrewko233 4 жыл бұрын
Wow, I'm just so glad you're doing more than just a conceptual course on quantum mechanics and as always your video's crystal clear and high quality. Thank you so much for what you do for all of us learners and I'm waiting for more.
@Yatukih_001 4 жыл бұрын
I have at least 5 books about quantum mechanics so I know what he´s talking about. It works in most computer game simulations of a universe so you can utilize it to create your own computer game.
@voidisyinyangvoidisyinyang885 Жыл бұрын
please tell me how to live my life.
@petersvideofile Жыл бұрын
@@voidisyinyangvoidisyinyang885 hayyyy drew :) I finally watched it. What was the important part you were directing me too ? It was something related to the amplitude being the square of two terms containing the imaginary components, right?
@voidisyinyangvoidisyinyang885 Жыл бұрын
@@petersvideofile sounds good.
@adahaholu9691 4 жыл бұрын
Yay, another video I won't understand but watch anyway.
@josesaldivar655 4 жыл бұрын
ada haholu Learn the "recipes" by heart and learn physics in a lab . true math is only the accounting system of physics.
@Jehannum2000 4 жыл бұрын
@@josesaldivar655 Nonsense.
@josesaldivar655 4 жыл бұрын
Jehannum Mindlessignorant
@gautamsah5075 5 ай бұрын
Agreed
@nono9555 2 жыл бұрын
Now I appreciate the 3 semesters of electrical engineering that taught me the mathematical language needed to be able to patially follow this at two in the morning instead of going to sleep so that I could be productive in the low skill job I have to attend at 8 in order to pay my bills. Your videos have the perfect pace and are super clear and on point. Well done.
@xonikkiecal 3 жыл бұрын
I am so happy you posted this. As a physics major there’s only so much conceptual videos will do for me. I can read the textbook multiple times but math needs to be applied (duh). Once you get to higher mathematics and higher level physics, professors don’t bother with showing examples anymore so we have to just figure it out like a physicist should do. So think god for these advanced mathematics videos for modern physics!!
@ivoryas1696 Ай бұрын
@xonikkiecal Not even a physics major (ME), but... *_right?_*
@CandidDate 3 жыл бұрын
The way he clearly and concisely massages the formulas really stimulates my math senses.
@KK-rg3nj 3 жыл бұрын
Ikr
@cguy96 4 жыл бұрын
Btw, at about 12:30, where you discuss the partial time derivative of Psi, your explanation was perfect, but I have found that some confusion can be cleared up by first rewriting e^i(kx-wt) as e^ikx * e^-iwt. Then, it is quite easy to see that e^ikx is a constant, call it C, so you are taking the partial time derivative of C e^-iwt, which of course is -iw Ce^-iwt, which is just -iw Psi.
@MegaXRadioMan 3 жыл бұрын
Amazing work! In my years working in physics, I've never encountered such a clear explanation of quantum mechanics with this level of mathematical rigor. This is an excellent stepping stone for a curious general audience.
@LunaticBiker11 4 жыл бұрын
Never delete these videos, i'll be back next year
@davidhigham1570 2 жыл бұрын
I learned more in one hour of taking notes, pausing, and doing the math at my pace with this video than I have in 8 weeks of struggling to keep up in my university course. I may just pass my midterm at the end of this week. Thank you!
@watchdatclip496 3 жыл бұрын
Thank you so much Professor Dave! I was searching for KZfaq videos that explained the mathematical side of quantum mechanics and your videos are honestly the only one I found, and the best too! The way you explain these are so articulate and perfect for anyone to grab the idea. Thank you again so much! Subscribed!
@rholin0997 3 жыл бұрын
I absolutely love how you introduce this material, and I agree, there really is no way to understand this material without the math.
@voidisyinyangvoidisyinyang885 Жыл бұрын
I wish he went into the de Broglie-Einstein Relation as Penrose does - realizing it is noncommutative nonlocality with mass originating from frequency.
@Yatukih_001 4 жыл бұрын
A truly enjoyable video to watch. Professor Dave feels at home when describing the concept of anything highly complex with regard to math and physics . He may find it a bit funny, but math fascinates me as well. Every day I read chapters from an over 1000 page thick Princeton companion to Mathematics, with the intent to just calm the mind and be more logical during the rest of the day. Momentum operators in quantum mechanics are indeed welcome and further research is required to decipher their remaining mysteries. Thanks for this!!
@OwenMcKinley 4 жыл бұрын
Haven't even watched, and I already know this is going to rock. Thank you, Professor Dave.
@tassosmanganaris9150 2 жыл бұрын
Woah. I really enjoy your drumming covers. What a surprising connection between channels
@karatheythemharkins2393 4 жыл бұрын
Did my physics degree at UNH ... after the classical stuff my next course was modern physics ... taught by Dr Heisenberg's son ... it was hilarious when he started talking about the HUP as it was obvious he wanted to spend as little time as possible saying his dad was in the textbook and he was not achieving that
@Jehannum2000 4 жыл бұрын
Wow. You were taught by Heisenberg Jr?! Cool. It must have been weird to see a Heisenberg talking about the HUP!
@karatheythemharkins2393 4 жыл бұрын
Jehannum yes, it was odd, but I was used to Heisenberg’s grandson hanging around my dorm (he was a business major) ... one day he launched a rocket signed by his grandfather, got it caught in some power lines, then just went inside .... meanwhile myself and a chem e were wondering who would be the first to try and retrieve it
@KK-rg3nj 3 жыл бұрын
That is so cool!!
@KK-rg3nj 3 жыл бұрын
I'm so glad I found this video. This is such an amazingly exhaustive work explaining operators. My physics class is running ahead of my math class so I have to watch youtube to bridge the gap. Thank you soo much for this video!!!!
@user-qx8zg4de6p 3 жыл бұрын
I really do love this math stuff. I'm telling you there are no videos talking about math of this depth
@MiltonRosso 3 жыл бұрын
I am so glad you're doing this, I have been wanting to learn about the math of quantum mechanics for a long time.
@thatomokoena4673 4 жыл бұрын
I'm no physics student but I love your videos and try to learn what I can. Thank you for your work Prof
@matiassantacruz5487 Жыл бұрын
These videos are a godsend. I am a second year student in university, and even though our professor is pretty good, the flow of lectures and of most textbooks introduce far too many concepts at once do not explain the rationale for creating them. Thanks so much Professor Dave!
@aleksanderkardyka6013 4 жыл бұрын
It just boggles my mind how scientifically sophisticated this man is! Kudos to you, Mr Farina! ^^
@unknownbeing8222 4 жыл бұрын
as a 14 year old watching this, i can’t thank you more professor davis.
@lakshmiamruthayechuri4005 4 жыл бұрын
Wow. Thats great to hear Young learner
@unknownbeing8222 4 жыл бұрын
Lakshmi Amrutha Yechuri always gotta educate yourself no matter what’s your age :)
@erikawimmer7908 3 жыл бұрын
@@unknownbeing8222 I am also 14 and I understand it at least a little bit
@josesaldivar655 4 жыл бұрын
Very cool , crystal clear. You know, while starting my grad studies, I wanted to film videos of each class as O had recorded audios on mini tape. I was dreaming on a computer based system. The internet days were at using menus or **** and a year later Netscape appeared. Now it is so good to have these accurate well pronounced lessons on demand , thanks to professors like Dave. Many thanks , and It should be in each And every lesson.
@rafaelcrispin5519 3 жыл бұрын
You sir. Are national treasure. Your explanations where clear and well thought out and I deeply appreciate what you are doing. Thank you.
@cliffordwilliams9597 3 жыл бұрын
Thank you so much for uploading this!!! I just finished calculus and am going into O-Chem and biochem; this will be a great way to keep up the maths skills !!!
@sathirapromodya6498 9 ай бұрын
The commutator provides information about the uncertainty or lack of simultaneous measurability of the observables represented by A and B. If the commutator [A, B] is nonzero, it implies that A and B do not commute, and you cannot measure both observables with arbitrary precision simultaneously. This principle is known as the Heisenberg Uncertainty Principle, which is a foundational concept in quantum mechanics.
@Gregegeg 3 ай бұрын
Maybe he explains this in another video, but how does A and B being communative effect observability? This is related to me not understanding why you are able to take the momentum of a position, and the position of a momentum. Let me know if you have any insight on this, any help is appreciated.
@mccawpa 4 жыл бұрын
Didn't understand most of this (understood a little) but had my mind blown by the calculations needed at this quantum level.
@subrajeetmaharana 4 жыл бұрын
Probably best video on internet to date. Thanks professor.
@lolygagger5991 3 жыл бұрын
it was really cool seeing something i learned in pre-calc like multiplying the conjugate of complex numbers being used in advanced math courses like quantum mechanics. thanks!
@geraldlarson5498 3 жыл бұрын
This video has helped tremendously with homework, thank you!
@criskity 4 жыл бұрын
I'm trying to imagine a flat earther attempting to understand even the most basic parts of this.
@cguy96 4 жыл бұрын
CNVideos oh yeah, I am going to say that most flerfers suffered radical cranial expansion at 0:20
@Yatukih_001 4 жыл бұрын
Easy peasy. I just have to use Wikipedia or other dictionaries. But even that is not truly understanding this. If I talk with my friends and we find out how to create computer simulations out of this, then you can say I understood something, even if I believed the world to be a globe.
@cguy96 4 жыл бұрын
Yatukih001 you could simulate this, without any understanding. Why do I say this? Because Prof. Dave is just listing all the relevant equations (or deriving them). So you could certainly simulate these equations, using various numerical techniques, but it wouldn’t mean anything. You wouldn’t have a concept of the initial or boundary conditions, and you wouldn’t know how to interpret the results of said simulation (assuming there were any meaningful results, which is highly doubtful). My justification for these claims? 30 plus years of large-scale numerical simulations of the Navier-Stokes equations on basin to global scales, which is qualitatively not that different from QM systems, and benefit from some of the very methods used to study QM systems. This is not something that you can just Wiki to understand (ok, maybe there is somebody out there who could... maybe).
@kevinclydeeguia2543 2 жыл бұрын
Im gonna come back in six months since im gonna study first the chemistry, classical physics and mathematics in order for me to understand this section of the playlist
@Jehannum2000 4 жыл бұрын
I've been studying this subject hard for more than a year and am just at the stage where I can follow at the level of this video. But somehow I hadn't realised that the commutator is itself an operator - so I've learned something. And for that I give a grateful 'like'.
@voidisyinyangvoidisyinyang885 Жыл бұрын
it's different whether it's Heisenberg or Schroedringer. Quantum PHysics Professor Basil J. Hiley uses noncommutative math - much better. NO need for a wavefunction.
@juliogodel 3 жыл бұрын
Thanks for going an extra mile on math explaining this! Well done!
@justin5455 3 жыл бұрын
I totally agree with your ideas. Math is the key to understand QM in depth!
@Sailesh004 2 жыл бұрын
Information overloaded... Everything is explained very clearly... Thank you so much...
@BigNes445 11 ай бұрын
You’re literally the biggest life savor, Professor Dave. I hope everything good that can happen to a person happens to you man
@estebancanizales3303 3 жыл бұрын
that was so good and clear wow everything clicked when watching this video thank you so much
@johnc4900 4 жыл бұрын
Prof Dave really do be dropping a better explanation of this then my university professor. Wish I had this video during modern last semester RIP. Anyhow thanks Professor Dave!
@parthverma6652 2 жыл бұрын
I actually finished the textbooks first to get a very vague idea of what quantum mechanics was... I was still figuring out the true sense and trying to fit it in my mind. But after this Lesson I feel like I have understood the basics clearly.!! Thanks.
@nikhil2453 Жыл бұрын
thank you so much for this video! You have no idea how helpful it is to me!
@MrZzzjjj 3 жыл бұрын
this is so good. Thank you Professor Dave
@tahoor4083 3 жыл бұрын
super awesome video, cleared all my doubts, loved it
@yourmom-nv9ui 2 жыл бұрын
You are so good 💕💕💕💕 thank you so so much for these lectures and I will watch all the ads in this video without a skip
@manpreetrana4484 2 жыл бұрын
Really amazing work 👏 🙌 thanks alot for this conceptual explanation.
@jalalabdallah7879 3 жыл бұрын
very good to Explain , Prof. Dave
@nyluong5427 3 жыл бұрын
Luckily I find this before my Physical Chemistry Exam tmr. Thank you Prof. Dave!
@leon_noel1687 3 жыл бұрын
Hey Dave, I will have Quantum Mechanics in University next Semester and I´m highly intersted, try to understand Operators for months, this video was extremly good for beginners. Thank you.
@JohnJoss1 3 ай бұрын
I've been reading Jim Baggott's wonderful book: "The Quantum Cookbook" and have got to the chapter on Paul Diracs derivation of the Wave Eqn with spin and Relativity. But I just couldn't find how out the momentum operator was derived anywhere. It'd been driving me nuts all day. You nailed it at around the 17 minute mark. Thank you kindly! Nope! I Still don’t understand this. I get p psi = h-bar k psi but I don’t understand where the h-bar comes from in partial by partial x of psi. I just get ik psi. So where does the h-bar come from in the partial derivative please Prof Dave?
@kimberlypena2898 4 жыл бұрын
How I wish I knew you during my college years. But thankyou for your videos.
@Ccaste1967 2 жыл бұрын
very very good explanations, Thanks
@HanBurritoz 4 жыл бұрын
18:16 Sel-adjoint and having real Eigenvalues are not the same. An operator can have real Eigenvalues, but still not be hermitian. For example the matrix A = (1 1; 0 1) has real Eigenvalues, but is not equal to A^T.
@yourmom-nv9ui 2 жыл бұрын
Wow you don't know how much i needed this video 😢😢😢😢😢
@geaninaalecu4567 4 жыл бұрын
Exceptional!
@cguy96 4 жыл бұрын
Nice! I was good with QM, it was QC that started my morning drinking.
@moeenkhan4803 Жыл бұрын
brilliantly explain
@rocketpsyence Жыл бұрын
Yes this is great. The math is stuff I had in college and isn't hard to brush up on. I think this is JUST right for me and is what I've been looking for. Everything out there seems to be limited to just conceptual explanations OR just throws you in the deep end with no background for where any of the equations come from. But this is just the right balance for someone like me - there's math, but you don't assume we know every single thing about the equations going in. I wouldn't trust myself to sit down and give a lecture on any of it, but for someone who can vaguely conjure up their old diff eq and linear algebra concepts while being bored in a waiting room somewhere this is fine so far.
@olafurjons Жыл бұрын
Extremely helpful
@HWC_CHEMISTRY 2 жыл бұрын
Outstanding
@zapp485 4 жыл бұрын
Underrated !
@wakeawake2950 4 жыл бұрын
Thanks alot!
@nikitavasilev7829 11 ай бұрын
Thank you! Maybe it is more for a physics student rather then for the general public, but that is exactly what i am and the videos are perfect!
@DAMN__________ 9 күн бұрын
This is such a good video
@shivamep-8757 Жыл бұрын
Best i ve found on KZfaq
@Boooommerang 2 жыл бұрын
Excellent job, wowww! One question: how much time do you need to prepare a video like this?
@rishavraj3099 2 жыл бұрын
can you please provide us with these slides or notes
@MS-cj8uw 3 жыл бұрын
Thank you prof ... its beautiful and amazing...... I have question.....What is the meaning of : the potential energy multiplied by psi in the Schrödinger equation ...what is the meaning of potential energy oscillation is there any meaning for that...thank you
@fernandoportal5422 Жыл бұрын
motivation to keep on with calculus and linear algebra
@QuicksilverSG 8 ай бұрын
Thanks for this nuts and bolts introduction to Hermitian operators, it lays bare the mathematical operations. It may sound hairsplitting, but in this context is it literally the case that "quantum particles are in several places at once"? While the application of the position operator on psi produces multiple solutions, each with a probability density of psi squared, in practice, only one of these solutions describes where the quantum particle is actually observed. Is it that describing a particle as being in several places at once is correct, but only on a statistical rather than physical level?
@speedspeed121 3 жыл бұрын
I have to say, this video and the following video cover the first chapter in Griffiths fairly well.
@lasbutious116 4 жыл бұрын
I believe the wavefunction we get after applying the operators on the wavefunction help us find the probability distribution of the operator type Is it ?
@xonikkiecal 3 жыл бұрын
Yea so you can find the probability of an electron being between an interval by doing an integral and then you can find which is the expectation value.
@user-pk9qo1gd6r 4 жыл бұрын
Will you talk about where these two operators come from? Especially the momentum operator which seems so random the way it is.
@alcoll1038 4 жыл бұрын
Look up Brant Carlson's lecture on this
@minaemad2393 4 жыл бұрын
Marvelous
@gnikkings Жыл бұрын
15:16 I would have liked for you to elaborate why you think all quantum objects can be expressed as exponential functions.
@priyadharshinivenkataraman5212 2 жыл бұрын
Hello prof dave .. I am studying 6th ... I have just found how to measure both momentum & position with a simple eqeation ..just shoot a photon on the sub atomic particle so find the speed of sub atomic particle + the photon's force on it... Then just subtract sub photons speed with sub atomic particle , then it will be easy to find position or momentum
@vikramnagarjuna3549 4 жыл бұрын
I love it...
@TJ-hs1qm 3 жыл бұрын
Why is Heisenberg's uncertainty principle expressed in terms of Δx and Δp instead of just Δx and Δv? Now, you have to measure mass and velocity instead of just velocity. Basically I'm trying to understand, why we are using the momentum operator instead of the velocity operator ( iow.. assuming m is constant, why deal with it?)
@nadiames8061 3 жыл бұрын
Merhaba, who wants that professor Dave makes videos about crystallography?!! Like
@aymenbk9138 3 жыл бұрын
in 16:47 is k the wave-vector or the wave-number?
@marckhanna861 2 жыл бұрын
Hi I am 10 years old and I like your videos I understand them all and can even do sums
@moulibeu Жыл бұрын
Sure you do
@gallapettisingaram5792 2 жыл бұрын
Thanks
@nicholspikos3136 2 жыл бұрын
Could it be true that something as simple as a single quantum particle has many or infinite degrees of freedom and once you have groups of particles clumped together into molecules you get many times less degrees of freedom and so on so that once you have regular sized objects...,....
@hassaanwaqas8896 2 жыл бұрын
I have a question. I fully understood the math until the end, I just don’t understand how the commutator of position and momentum calculated lead to the uncertainty principle
@harrytruman5700 4 жыл бұрын
Hi Professor dave
@alexdred5750 2 жыл бұрын
Dude do you really know any good books for quantum or modern physics
@zohrebashtani2990 2 жыл бұрын
perfect
@overlordprincekhan 2 жыл бұрын
BTW, is that "e^(ikx-Ωit) " derived from fourier series?
@kjl3080 2 жыл бұрын
I recognized it as the heat equation
@yourmom-nv9ui 2 жыл бұрын
Guys don't skip ads on his videos if you are not supporting his patreon ..he is actually putting alot of efforts and I would kill to be his student 😓😓😓😓
@lcy6434 Жыл бұрын
As Barrier in prognosis is as difficult as Magellan’s voyage using Celestial Navigation before any civilization’s comprehension.
@venkataramanadasari7465 4 жыл бұрын
Hi dave
@dolfanatic314 4 жыл бұрын
Damn I wish I knew you years ago. Math always clicked for me. Some kids in high school and I would get a different test. Even kind of taught my friend way back in 1981. Flat Earthers tell me I impossible because no one can live this long. I had all the numbers. And flushed them a few years ago. The symbols I know what they do, but cant get past that. Be well keep up the posting
@garysamuel9521 Жыл бұрын
i times i is 1 not negative 1, correct?
@ProfessorDaveExplains Жыл бұрын
No it is negative one.
@weesaikim6090 4 жыл бұрын
Hey prof dave, why don't we ever see your face anymore? I definitely miss the old videos with you explanining with a whiteboard :)
@ProfessorDaveExplains 4 жыл бұрын
It's because of COVID! KZfaq studios is closed, and that's where I normally shoot all my content, so I have to make do with what I can get done at home, and I don't own a camera. So I do a little bit of webcam stuff, but for the rigid tutorials right now I'm just doing audio only.
@Yatukih_001 4 жыл бұрын
@@ProfessorDaveExplains At home in Iceland I don´t wear any mask. But out of respect for the feelings of those who are terrified of covid I try follow every rule recommended.
@freddan6fly 4 жыл бұрын
@@Yatukih_001 Wow you live in Iceland, has just come off the polar day (impossible on a flat earth) and still believe in flat earth, that is really embarrassing stupidity.
@hwetherell6250 4 жыл бұрын
Just for clarity, since it does not detract from what you're saying: around 7:20, you mean "linear operators", not operators in a general fashion. There are non-linear operators.
@benmcwhirter4566 2 жыл бұрын
You problem won't understand but may get something from it anyway. Proceed's to explain operators so. I better understand c++. Thanks
@philtoa334 4 жыл бұрын
Not bad :)
@freshely9309 3 жыл бұрын
Oh yes I am very much aboard the quantum train, but unfortunately I don't know exactly where on that train 🤔
@utkarshraj3272 8 ай бұрын
👏
@lexastron 3 жыл бұрын
I don't understand all this particle-wave duality concept. What actually happens when elementary particle hits the detector? A literally "real" particle of matter reveals its position when it hits the detector and transfer its kinetic energy to measurement? Or maybe it's more logical that this quanta of energy was literally a field oscillation all the time. But due to the fact that energy absorption occurs in quanta-sized portions, it can be absorbed in only one point, in which the whole energy of this wave transfers to the detector? Why must we use this ghostly concept of particles? :)
@elivaughan1192 2 жыл бұрын
Haha. I'm that guy. I'm the one that saw the prelude of this and said "pssh. I dont need to go back and watch those others. My math strong.". 10 minutes later... uhhh
@alexvila6611 4 жыл бұрын
I suppose it is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail.
@AAAAAAAAAAAAAAAAAAAAHH 3 жыл бұрын
Bad ass
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