I appreciate these lectures being online.

@atharvakanherkar9502

3 жыл бұрын

And free

I would like to compliment the camera man for his fine work. Also whoever is responsible for recording the sound did a great job. It's so important to be able to hear and see these lectures clearly. My thanks also to MIT for making this content available.

I love this form of explanation. It is so complete. And I love that the facts and reasoning are explained in a human-centric simple form, where so many others throw a bunch of fact at the screen. Thank you! I will use this information in the most powerful way. I have tried to wrap my head around the supposedly simple idea of linearity for a long time. Somehow this shifted me over my preconceptions.

There are some people who are perfect communicators of complex subjects. My calculus teacher, Martha Kasting, was one such person. She would smile the entire time as she described Green’s Theorem, or she would say, “Isn’t that a pretty equation?” Dr. Zwiebach is another.

Thank you MIT OCW and all MIT staff!

I'm Sido Rodrigues Brazil I really like Quantum Physics Classes. Very important to know quantum physics. Teach everything the universe knows and you gain self-knowledge about everything. Great series of really useful lectures on quantum mechanics. I am also very grateful to MIT OpenCourseWare and Barton Zwiebach... etc...

I feel illuminated. A clear and concise lecture by a lecturer who comes across having an authentic passion for learning and understanding. Thank you 🙏

As someone who works in (classical) fluid mechanics, I can confirm that it's very very nonlinear.

@chuuuu1131

4 жыл бұрын

Can you give an example?

@frun

4 жыл бұрын

Does it look like electromagnetism? I think he meant classical mechanics.

@LifeForAiur

4 жыл бұрын

@@chuuuu1131 Not him, but in fluid mechanics, to quantify the deformation of a fluid particle in a continuous medium you need something called a stress tensor, which is a 3 by 3 matrix describing the direction of the stress imposed and on which "face" of the fluid particle it is acting on. Check out the Navier Stokes Equation expanded out.

@MrMathjordan

4 жыл бұрын

Agreed.

@user-fb4zo8wd5n

3 жыл бұрын

True. Many applied mathematicians research in the field of fluid mechanics.

This is actually an excellent class. It worth's its length in Gold. Thank you very much

First time I’ve ever heard the process of QM explained outright, every professor I’ve ever had on the subject just jumps right in and it’s hard to grip without foundational information.

MUCH THANKS MIT

Thank you. Great teacher. Easy to follow.

@Anb-ng2ou

4 жыл бұрын

How is called this teacher pelase?

@ZapytajRedditPolska

Жыл бұрын

@@Anb-ng2ou what are you doing here if you have problems with reading description?

@nichokind5233

2 ай бұрын

@@Anb-ng2ou Dr. Barton Zwiebach

thank you MIT AND ALL FACULTIES FOR PROVIDING INTERESTING LECTURES ON QUANTUM MECHANICS...

Very excellent open course on QM, thanks MIT professor!

I'm from India.... great thank you mit gives the online courses...little tweak are arises...but most of the phenomenal are not predicted..which means my life time scenario is the one of the examples...some atoms are vibrated...but no losses. After some times the illusion are visible... 🤔

Nearly 200,000 views on the first video, and the second video only has a quarter of that? Shame so many people gave up already

@HighestRank

4 жыл бұрын

Brandon Smith maybe it was just a review which they needed, I myself got this only as a recommendation even though I’m not a subscriber to OCW, and wouldn’t have expected anyone who didn’t realize there is a second part because they weren’t told in the video to go looking for it or to recognize it if it had bit them in the nose.

@MegaFunkysoul

3 жыл бұрын

They were looking for pseudoscience

@abrarfaiyaz6503

3 жыл бұрын

Maybe they moved on to the ocw site.

This professor is amazing.. Though my stream is not linked with this subject but then also i have seen the whole video :)

Great teaching ❤

Thank you so much!

You are great.

Thnx to mit n your staff to spread your valuable contribution in enhancing the concept in worldwide.. Respect n love to you all guys.....

Phantastic lecture!

@lepidoptera9337

16 күн бұрын

Not really. I am beginning to wonder how this guy made professor at MIT. ;-)

@MITOCW Is this the same room where they did the old 2013 QM course, but renovated??

@mitocw

7 жыл бұрын

Good eyes! Yes, this is the same room where they did the 2013 version of the course. :)

Thank you for share!

Thanks

What a great intro

Good lecture

thank you

benedict cumberbatch in disguise

@Shooo117

24 күн бұрын

Bruh😂

If schrodinger's equation is linear in any case by default, is it not possible to observe nonlinear behavior in quantum system?

Where and how does the non-linearity get introduced in classical mechanics when quantum mechanics is all linear?

Can't we use linear qm to solve 3 body problem

Thanks for confirming something I've been wonderimg about for some time now! You've got no idea what you just helped me out with. 👍😁

hmmm i guess quantum mechanics is linear because the potential operator is applied ("multiplied") to the wavefunction, instead of the potential being an arbitrary function *of* the wavefunction, as in classical mechanics

@ 9:30 he talks about Schrodinger not knowing what the wave function is. How did Schrodinger come up with this equation in the first place. Professor Zwiebach doesn't offer an explanation of how Schrodinger came up with this equation. But Schrodinger must have had reasons.

In what extent can someone assert that classical mechanics or quantum mechanics is linear or not? Is in regarding to the description of fundamental interactions and not merely idealized models? Because a classical harmonic oscillator is a linear system inside classical mechanics and systems that respect Ginzburg-Landau equation are non linear examples in quantum mechanics. Why those aren't consider counter-examples to the thesis defended in the video?

Mister Zwiebag, you absolutely rock! Explaining complex stuff simple is a trait of true genius!

I am from Bangladesh Love Quantum mechanic

Dynamic quantum variable, wave function

Amazing👍 Can anyone say whether these are graduation or postgraduation classes? Or anything else?

@pranjalsharma3370

2 жыл бұрын

@pippo Thanks!

The Hamiltonian operator may contain a potential term. So how is the Hamiltonian always linear?

Arent you the dean of the university of architecture in copenhagen?

I think I am going to treat myself to hotdogs in my mac and cheese tonight.

@spencersabet8601

3 жыл бұрын

I respect that. Have fun

@ProgressiveTeen

3 жыл бұрын

How evil. Torturing animals for your tongue's evil delight.

@FreezerBurn.

3 жыл бұрын

@@ProgressiveTeen ... kind Sir, sadly you are mistaken. Mac and Cheese is not an animal.

Why is the Schrodinger equation linear when the Hamiltonian depends on V(x), and earlier he said that V(x) can be arbitrary? The quantum harmonic oscillator is a perfect example of a nonlinear potential and as far as I know you need special techniques like Hermite polynomials to solve it.

@commonlistener87

18 күн бұрын

Linearity depends on the dynamical variable you’re solving for. In the example the lecturer presents for Newton’s equations, you are solving a second-order differential equation for the “variable” x (which is a function of time). The equation is nonlinear *with respect to x* whenever V’(x) is nonlinear with respect to x. In the case of Schrödinger’s equation, by contrast, you are solving a partial differential equation for psi (the wavefunction), not for x. You’re right that the Hamiltonian has a potential term V that depends on x (often nonlinearly), but V doesn’t depend on psi, and it’s psi that you’re solving for.

Aren't maxwell's equations only linear for some materials?

For some reason I keep watching this guy even though I don't understand ßhit of this

hamiltonian has potential energy inside and why it is linear?

@AbhishekSachans

2 жыл бұрын

Because potential energy is not a function of the 'wave function'- the independent variable in schrodinger's wave equation (or its derivatives); unlike in Newton's equation of motion in which P.E. WAS a function the independent variable(s) e.g. x in general.

(Reproduction/Feed/Reasoning) decanted selfover hexagon...

thanks sir for this amazing lectures but can any one give me the notes of the course please?

@mitocw

4 жыл бұрын

The lecture notes are available on MIT OpenCourseWare at: ttp://ocw.mit.edu/8-04S16. Best wishes on your studies!

@abubakarejaz5539

3 жыл бұрын

Hey U a physics student too?

Can anyone elaborate a bit from @2:20 to @2:33. What did he mean? Where did that graph came from?

@NoName-vq6cg

4 жыл бұрын

Graph of potential energy over time. (Potential energy meaning the work that force has to do. Force × distance) The derivative is the force acting on it at a specific time. Like if a ball is rolling down a hill, hes basically just saying that because there's mass, gravity would be pulling it down, and it loses potential energy as it gets closer to its destination and force is used. So the force is the negative of the derivative of potential energy.(someone correct me if I'm wrong)

Can someone explain what is potential V of x? I'm noob in quantum physics. Does it mean a kind of potential which is providing force?

@bencegabor9228

3 жыл бұрын

Potential V(x) is a classical quantity, whose negative derivative is force. For example: en.wikipedia.org/wiki/Gravitational_potential or en.wikipedia.org/wiki/Electric_potential#Electric_potential_due_to_a_point_charge

@nsudhir_here

3 жыл бұрын

@@bencegabor9228 thank you sir

4:39 Is time is dynamical variable? what is definition of dynamical variable?

@friendlyone2706

3 жыл бұрын

@@damariscalleros4631 but time changes, sometimes

5:13 how is Hamiltonian operator linear? Since it also contains potential energy term which need not to be linear.

@zacharythatcher7328

4 жыл бұрын

Kaushal Jain the potential in the Hamiltonian can be thought of as a set of values that span relevant space (a normal line or surface over space) that the wave function will be multiplied by at every single one of those points individually. So the wave equation (the input) will be transformed in essentially a multiplication style operation. Multiplication is linear, and so is the “potential operator”. If the potential was somehow squaring or logging the wave equation, that would be nonlinear, but that is impossible. The potential isn’t that weird. It just multiplies the wave equation by its own predetermined values, which you could do before or after multiplying by a constant and get the same result.

@aryasingh8173

3 жыл бұрын

@@zacharythatcher7328 wow

Sir can a wavefuntion determine the dynamics of a macrobody?????or it is just applicable in cases of microbodies

@farooq8897

6 жыл бұрын

It can.. But Classical Mechanics is a good approximation and easy to use..

Explain 0:56 to 1:05 by example

Hamilton?

9:22. Why is one wave function unable to explain both spin up and down state of e-?

@benwincelberg9684

3 жыл бұрын

Initial conditions aren’t given

Can you catch the sensation of simultaneity, can you do 1+1...

I have a question, isn't Hamiltonian operator also a non linear operator, because it also contains Potential term which may be quadratic or cubic depending on the condition. Thus, isn't then Quantum mechanics also, non linear in nature. Please, explain if I am wrong.

@sylvenara

Жыл бұрын

While the potential energy term in the Hamiltonian operator of quantum mechanics can be nonlinear, the dynamics of quantum mechanics are fundamentally described by a linear equation, the Schrödinger equation. Therefore, quantum mechanics is considered a linear theory.

@AlexBlade27

Жыл бұрын

@@sylvenara ok understood. Thanks for the help😊

explain 0:53 to 1:07 by example

Good

Ojala algun dia regrese Barton a la Fiee para para una clase de estado solido 🙌

I didnt know i had spedup the videos (to 1.5x) until I read the comments. Oh man, he speaks too slow to the point that his class could be boring. Thankfully it is an online course where you can set the speed, and also for some people that are not familiar with the language and might want to slow it down ;) Greetings from Peru

You can aquire all thie knowledge for free.You may even sit down in the lecture und visit all classes and pass the exam.But if you want that piece of paper which says that you did all of that you have to pay thousands of dollars.

The size of simultaneity...

It is linear iff a linear relationship exists

9:35 How did Schrodinger come up with his equation before there was any physical interpretation for the wave function? What did he try to derive? What was his starting point?

@durgeshgaikwad741

4 жыл бұрын

When de Broglie proposed the idea of matter waves, Schrödinger tried to find an equation which could describe these matter waves and hence came up with the famous Schrödinger equation

@lambda2693

2 жыл бұрын

it is quite easy. you just have to prove that what the classical operators become in qm. like p=-ihbar d/dx or E=ihbar del/del t

@infinity-and-regards

2 жыл бұрын

@Lambda that doesn't sound easy at all, could you elaborate?

@lambda2693

2 жыл бұрын

@@infinity-and-regards look finding the operators is tough but the derivation of the equation is very easy if you know the operators. okay look i will derive it for you but i will assume the operators if you want the proof for why the operators are equal to what i am assuming you will have to look it up as the proof is very long. E=KINETIC ENERGY + POTENTIAL ENERGY KE= P^2/2M. PE=V(X,) LET US QUANTIZE THIS EΨ=P^2/2M Ψ +VΨ NOW EΨ=Ih/2π dΨ/dt. and p=-ih/2πd/dx Ih/2π dΨ/dt=(-ih/2πd/dx)^2/2m Ψ+VΨ Ih(ΒΑR)dΨ/dt=-h(BAR)^2/2m d^Ψ/dx^2+VΨ AND YOU HAVE DERIVED THE SE. YOU CAN DERIVE ITIN OTHER FORMS BUT THE PROCESS IS SAME. THE REAL CHALLENGE COMES IN PROVING THE ASSUMPTIONS AND YOU TO USE BRA'S AND KET'S FOR THAT. ALTHOUGH THE PROOFS ARE GIVEN IN SOME TEXTBOOKS BUT ARE VERY COMPLEX. EVEN GRIFFITHS DOES NOT GIVE THE PROOF

Very good teacher!! I have a question : 3:34 Why x squared is not a linear function?

@mateusmarinho72

Жыл бұрын

f(x) = x² f(a + b) = a² + 2ab + b² f (a) + f (b) = a² + b² So f(a+b) is not equal to f(a) + f(b), therefore it's not additive. So it's not linear.

@kostasargiris748

Жыл бұрын

@@mateusmarinho72 yes, okey, thank you very much!

@urpisarmiento5385

3 ай бұрын

​@@mateusmarinho72muchas gracias, entendí la explicación.

Whatever it is it's non-linear, and it is the easier explanation. Maybe he says this later Im 30 seconds in.

Excellent lecture Sir. Thanks 🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏

Where is the teacher from?

@carloveable1

4 жыл бұрын

He studied at my University in Peru (well known in Peru as UNI) at the same Faculty than me and he finished (Electrical Engineer career) I believe in 1977, then he came to America to follow Master and PhD. degrees.

Why can we assume the Hamiltonian is a linear operator? Isn't it another measure of potential, and theoretically could be made some non-linear result?

@LusidDreaming

4 жыл бұрын

I don't know enough about the Hamiltonian to directly answer this, but in general an operator is linear if it satisfies the following two conditions (O is an operator): 1.) O(f + g) = O(f) + O(g) 2.) O(c*f) = c*O(f)

@frun

4 жыл бұрын

@@LusidDreaming yes. I think that's the definition.

@fredrikj8491

4 жыл бұрын

The difference is previously your solution was in terms of x(t) and the potential depends explicitly on x. Now your solution is in terms of the wave function, of which the potential is not a function. The Hamiltonian is a linear operator on the space where the wave function lives. The potential is not a function of your wave function.

@ericsmith1801

4 жыл бұрын

@@LusidDreaming So there cannot be time compression to satisfy linearity... experiments seem to suggest that in addition to spatial nonlocality there is temporal nonlocality involved in entanglement. I doubt that changing the inertial frame of reference will get rid of such nonlinearity.

Can anyone help me understand what the T-like symbol really means in the derivative equation?

L. Rahman Grand Unified Model

Han Solo is now a physicist? Damn...

3:49

Yes professor, I found the tutorial irrelevant since I’m no where near being a physician.

Why is 2nd law for newton not linear wrt Potential? Partial derivatives are linear and so are the normal derivatives...

@AbhishekSachans

2 жыл бұрын

Because, say for one dimension, x is an independent variable of which potential energy is generally a function so that gives you a non-linear differential equation. That's it!

sir how force is equal to the derivative of potential...Sir as I know the force is equal to -du/dx (rate of change of potential ENERGY W.R.T X) not potential.....

@mysteriouspandey3450

4 жыл бұрын

Pehle basics clear karo Bhai baadme quantum ki lectures samjhoge

@riturajanand7133

4 жыл бұрын

@@mysteriouspandey3450 Thanks sir for your advice, please answer to bta dete doubt ka

Hi

3:31 What is V(x) ?

@Inserthandle-ff6jw

22 күн бұрын

Velocity along the x axis

Within 25 years you have to get a PHD. Only then by 30 you can get a job and support anyone. Just because your life is 100. And atleast relax for some time. Mostly when you get to an industry it is all apps of the learnt. Whether you remember or not is not much of an issue because you can recall most.

CLASSICAL MECHANICS IS NONLINEAR AND QUANTUM MECHANICS IS LINEAR THEN HOW CLASSICAL MECHANICS IS APPROXIMATON OF QUANTUM MECHANICS.

free knowledge hooray

@Adam-cn5ib

4 жыл бұрын

why pay when you can not pay? right?

alright he reminds me of dr. peyam

Orgullo peruano

QM(quantum mechanics) is linear? where is the laws of physics that says it is, we dont truly know if QM is linear, but the probability representation of psi or ANYTHING is ALWAYS linear, because we MADE it linear so that it could be solvable, this is the ONLY way we could even TRY to solve for the slightest bit. "it is linear" and "we MADE it linear" are two different things. the initial value problems of non-linear classical mech is the SAME as the boundary problems of linear probability representation in quantum mechanics.

@lepidoptera9337

16 күн бұрын

It is linear because the quantum mechanical ensemble consists of statistically independent experiments. That's an assumption. Since we do not have an actual ensemble in real life but only the repetition of the same experiment, the statistical independence of the data set that it produces has to be tested. It will usually work out fine for e.g. the photon flux from a thermal light source, but it will show very strong temporal correlations for a laser source. So you are not completely false in saying that "we made it linear", but the naive assumption that every quantum mechanical system obeys that linearity is incorrect.

You don't need any of this. Just go to Vegas on weekends and play black jack.

@Greato_

10 ай бұрын

Wtf

Newton's is non-linear because potential could be non-linear function; ok! But Maxwell's is linear...couldn't potentials A and V be non-linear?

@HighestRank

4 жыл бұрын

dougie v yes, Aa is easy to see, but Vv will always be made using straight lines.

Interesting thing. First video has 2x more views than second :D

I have some doubt about the view that professor mentioned in the lecture about the relation between the many body equation solving difficulty and the linearity of equation.And I think the linearity of shrodinger equation provide us a possible way to solve the superposition problem, which is a one body problem! So, I do not agree the view that the nonlinearity of Newton mechanic equation make three body problem hard to solve.I have not tried to solve many body problem by shrodinger equation or newton mechanic equation, so my point might be wrong.I hope somebody could help me to figure this out.Thank you:)!

Somewhat vague definition of the difference between linear and non linear.

Sir . I wanted to ask .............we know that a theory has numerous equations in it working all together to state one point .Now if we say that a theory is linear then does it state all the equations of that theory to be linear or there is a possibility for only a few to be linear ???????

@friendlyone2706

3 жыл бұрын

The moment a non linear factor is introduced, everything affected by that nonlinear factor becomes nonlinear.

I'm from Iran.I love quantum physics and the other parts of physics and absolutely I go to the MIT university.

for a second there i thought he was Harrison Ford

Chaos theory is non linear. Nullo space is linear

(steepled hands)

this continuous montages and cuts through the video made my upset because i want to know everything he says like the real lecture :(

Nothing is linear or non linear, it depend on how you consider it., observation,. When you see as human being you will try to explain like all excited scientist.

@benwincelberg9684

3 жыл бұрын

?

👍👍👍👍👍👍👌👌👌👌