Can't you tell somebody that loves and breathes their subject? No notes or materials, just straight out of the head. Brilliant man

I love how his 5 minute explanation of why the ODE is hard turned into like half an hour. 😂

My gratitude to your advice. The original plan was only to upload a few of them and refer the audience to the official PSI website. There are 15 in total. And upon your request, I shall upload the rest asap. Cheers!

Wonderful to see someone teaching a super hard subject with a smile. Dr. Bender's smile is infectious as can be seen on the faces of the students.

Ladies and gentleman, that individual is an outstanding teacher. It's one of those talented individuals who really shows the difficulty of the theory without omitting details. (D+tanhx)(D-tanhx)y(x)=0 should be the factorization instead of (D-tanhx)(D+tanhx)y(x)=0. Operators are not commutative in general. Aside of that perturbation series is the only way we have for approximations when we deal with the Schrodinger equation. Frobenius series are used for special problems such as Bessel, Legendre, Hermite, Hyper geometric, Laguerre differential equations.

Once again thanks a lot. I watched all the 8 lectures, its amazing. I'm a Phd student and I was stuck in my research because of lack of knowledge in Perturbation theory. After studying the lectures I feel confident and wish to watch the rest lectures asap. You can't imagine what magnitude of help you have provided to me and others like me.

I've them all uploaded. Enjoy!

@roberthuber2770

3 жыл бұрын

Thank you!

@extraterrestrial46

3 жыл бұрын

Thank u guy

11:10 It took me a while to process this. Wow. That was so smart of her. Going 899=30^2-1^2=(30-1)(30+1)=29x31. And the fact that she probably thought to do that just from seeing him write D^2-1.

This prof. is really well prepared for lectures.

I wished I learnt concepts like this in my engineering math classes

At 27:20 the geometric meaning of the substitution of y= Q (w'/w) is asked about. If you look at the term in parentheses you see a function divided by its own integral. This is what you get when differentiating ln(w(x)) with respect to x, for any differentiable w(x). Recall that Q is chosen to make the quadratic terms cancel and it evaluated as a number not a function. The substitution is then equivalent to saying, y(x) - Q(x) = (d/dx) ln(w(x)). Integration of both sides and solving for w, gives, w(x) = exp[ ∫ (y-Q) dx]. The geometric meaning is *exponential*. Take its derivative and divide it by the original function and what you get is (y-Q), where Q can be chosen. It is a substitution not so different really from an integration factor, which is comparably "rigged" to create the symmetry which reduces a nonlinear DE in y, to a linear DE in w.

used his book in grad school to learn the math for doing Quantum Chemistry. very nice to hear his lectures. Bender and Orszag is a classic for a good reason.

@lugia8888

Жыл бұрын

Sorry to hear that

I've been trying to get into perturbation theory since october with a good dozen of books, which all explain the matter quite well. but prof. bender does it with so much heart and patience,...such a great person. wonderful, thank you for uploading. so much help, for a small times information systems guy!

@irenebrennan

6 жыл бұрын

ditto he even created order out of the complete chaos of my mind

The way he perturbatively solved the 2nd-order ODE is exactly the proof of the Picard-Lindelöf theorem...

Excellent professor! Before watching this video, I struggled to figure out the way to solve the 2nd order linear differential equation. However, the lecture here gave me the clue I need to successfully work out my problem.

Me Agrada mucho que el Profesor Bender explica con un sistema facilitador para que uno se motive a investigar por nuestra propia cuenta, siendo que el solo da las Pautas en forma Muy Amigable,y me gusta mucho su Método. Yo entiendo Inglés.

Chini’s equation is the most general analytical solution I’ve seen for this problem, but that requires special relations between the function coefficients.

Best lectures on mathematical physics

My mind is blown like never before! Marvellous!

Amazing lectures! However, the experimental tuning of \epsilon for transiting "smoothly" from E_1 to E_2 is misleading: in an experiment \epsilon always remains real, hence the gap is always finite. Hence the adiabatic theorem of quantum mechanics tells us if we start with E_1 initially, we will always stay in E_{1}(t) at all t if we are sufficiently slow (the scale of slowness is given by the inverse of that gap which is finite). Hence tuning \epsion back and forth won't take you from E_1 to E_2 smoothly (it will just produce a hybridization of both, the weight of E_1in the superposition being closer to 1 for slower drives). Moreover, one can always draw the branch line in a way so that one doesn't have to cross it while tuning a real \epsilon in this case. Finally, crossing a branch point even in real parameter space (where there are true accidental degeneracies in > 2 level systems) can hardly be called a "smooth" process - but that's just terminology :).

This is a little more interesting than I thought it'd be.

i watched this while stoned and felt like a genius

@EvaPev

4 жыл бұрын

I felt like a genius without being stoned. That's cos he is just SO SO good!

@nylehaywood2471

4 жыл бұрын

Ya

@nylehaywood2471

4 жыл бұрын

@@EvaPev ya

@pikiwiki

4 жыл бұрын

hats off

This is actually really good. Even though I'm 15 I could still understand everything he was talking about.

Very much like this video！This teacher is fantastic！

Perimeter Scholars International, an MS course program held in partnership with the University of Waterloo

Mistake at 12:00. The minus is in the front on second Tanh(x).

awesome lecture. for once, also a really smart audience in general :)

Very interesting, thanks a lot!

@ 7:24 that is priceless expression from the Prof.

thank you sir u r a life saver. next generetion education!

Wow. Great lectures completely marred by the placement of the microphone(s).

So much ambient noise. Teacher is great!

energy levels are smoot and continuous always, they represent distrubutions spaning all space, as such they must be smoot and continuous, but not always discrete

marvelous! please refer some easily available text for material.

Very intellegect topic welcome to you

super...

Maybe yes. However, i wasn't able to achieve it online. Please refer to his old book about asymptotic series, if available. ^^

Wow, this series is enlightening. Much better than Susskind's.

29:22-30:38 The principle of conservation of effort.

@morbidmanatee5550

8 жыл бұрын

We called it the "Conservation of Difficulty" :)

@AndDiracisHisProphet

8 жыл бұрын

One of my professors called it "Conservation of mathematical ugliness"^^

@DanielCwele

8 жыл бұрын

LOL... Mathematical Ugliness?? Seems a little harsh though, doesn't it. Linear equations are fairly regular and have fairly regular solutions. While they are not easy to solve, they are still quite beautiful. I often associate "mathematical ugliness" with hyper- non-linearity and "chaos". Would you agree? and, more importantly, do you think Dirac would agree?

@DanielCwele

8 жыл бұрын

@Garrett Van Cleef, Lol.... That's a perfect description.

@AndDiracisHisProphet

8 жыл бұрын

Harsh, but perfect^^

At 12:15 the professor factors D^2 - 1 incorrectly. He should have written coth instead of tanh. Check the calculations. Excepct for this small error, he is correct otherwise.

56:33 why cant we add \epsilon to the term (x^{2}/4 + x^{4}/4) together ? like \epsilon(x^{2}/4 + x^{4}/4) ? we already know how to solve the (x^{2}/4 + x^{4}/4)=0 equation that is just easy second order equation. is it something to do with the sudden vanishing of roots or something ?

In just going to keep on studying.keep studing students.

As an undergraduate doing Maths some of your lecture makes sens to me. However, may I share with you something I thought of: the speed of light can easily be reduced to a series of square roots. In my thinking, this corresponds to energy levels. I would welcome a response from you if you have the time. Thank you

@williamchurcher9645

4 жыл бұрын

Hi, graduate maths student here. What do you mean by a series of square roots?

1:08 What about to use \epsilon^2 instead of just \epsilon?

How to find the coefficient of the ground state a(0)=1/2 and phi(0)=e power of -x sq/4 (57:44)

@welcomeblack

4 жыл бұрын

It's the energy and wavefunction you find when you take the quartic coupling to zero, i.e. the usual first energy and wavefunction of the quantum harmonic oscillator (see wikipedia page)

Great content. But 360p?? Really?????

Power series combined with green"s function ?

I don't understand. Why can't we put y=ce^rt when solving 2nd order linear ODE like we learn in calc3 cass? With the Wronskian youknow? I'm very new to this. Could someone help me please? Thanks :D

@robertmines5577

3 жыл бұрын

The solution y = c1*e^(r1*x) + c2*e^(r2*x) only if the coefficients a(x) = c and b(x) = c (constant). In these problems, a(x) and b(x) are non constant functions of x.

Why does he say limited domain what does that mean, and why can it only be solved as such

Also why did the problem need to be integrated in pairs

Where does the closed-form expression at 47:00 for the sequence of integrals come from?

@waldonumberone

7 жыл бұрын

Answered my own question: comes from an easy induction proof on iterated integrals. If there are n nested integrals of the form \int_{0}^{x_n) ( \int_{0}^{x_{n-1}} ( \int (... (\int_{0}^{x_1} dx_0) ...) dx_{n-1}) dx_n, the result of the integration is (x_n)^n / n! In the lecture, n = 2n.

@yuvalmeir2263

4 жыл бұрын

@@waldonumberone thank you - and for anyone else who got confused over why it's 2n - we have n double integrals

which university is this ??

If Feynman had such a blackboard, the infinities wouldn't keeping popping up!!!

did the guy at the end ask about new possible lepton?

Furthermore how did he derive the parameters for the initial value of the An segment as An=0 and A'n=0?

@jpaultelchannel1702

2 жыл бұрын

Quantum mechanical system: Those are the boundary values. Consider a harmonic oscillator, the system of a brick attached to a spring, at t=0. The brick is at rest and the rate of change (speed) is zero. He was solving a perturbed QM harmonic oscilator. So, a0=0 and a'0=0

you can find some of this stuff in his book Advanced mathematical methods for scientists... Watch read... REwatch

I couldn't understand the initial conditions for An (around 41:30) An(0) = 0 An'(0) = 0 for n>0 can somebody help?

@Idkwhoiamlolrawr

5 жыл бұрын

The a + bx is already satisfied by the conditions that he put on the board, and thats the '0th' coefficient, so any coefficient passed that must = 0 in order to have the whole series still satisfy the initial conditions

@nic3589

3 жыл бұрын

I know this is old, but for posterity, I'd like to answer. It's easiest to see by imagining that it is NOT true. Suppose a1(0) = c != 0. Then, the series expansion includes a c \epsilon term which cannot be cancelled out by anything else since the boundary condition does NOT depend on \epsilon. Hence, c must actually be 0.

is there a text that goes along with this lecture?

@jpaultelchannel1702

2 жыл бұрын

He is working at the introductory level. Google "Perturbation Theory Physics pdf" for other introductory text. Most books are "hard core mathematics" on this topic so texts are rare. However I found one that begins at a comfortable level like this Prof. www.iust.ac.ir/files/fnst/ssadeghzadeh_52bb7/perturbation.pdf

Hi zicheng5261941 first of all I thank you for making this video available. However, I was wondering that is this list of 8 videos complete of there are few more additional ones. If so can you also upload the rest. Thanks Once again

Ya

Carl bender : we will reach a climax 5 minutes later Carl bender : all you have learned is garbage ( he continues by saying unless you make sense out of it )

are there any problem sets to complement these lectures?

@adandap

9 жыл бұрын

I couldn't find any, but Bender has a book on the subject that apparently has lots of problems (caveat: I don't own it). www.amazon.com/Advanced-Mathematical-Methods-Scientists-Engineers/dp/0387989315

@isodoublet

9 жыл бұрын

I own it. There are indeed lots of problems. Caveat: there are no answers.

energy levels are smooth and cont. only in pert. theory with Riemann surfaces, or at all? Probably only the former.

At 3:50, why do we want the z' terms to be 0?

@waldonumberone

7 жыл бұрын

Because we wish for z to satisfy the Schrodinger equation, which has no first-order (z') term.

What's the type of 'w' in 'w`` + aw` + bw = 0'? :o Is it 'ℝ → ℝ'? If so I guess the types of 'a', 'b' and '0' is also 'ℝ → ℝ'?

does someone know at which university level it was thaught?

@aedin6397

4 жыл бұрын

It looks as though (from the first lecture of this series "Mathematical Physics 01 - Carl Bender" at minute and a half in) that this is a lecture being given at the Perimeter Institute by Dr. Bender, who is from Washington University (in St. Louis). That'd be my guess, but yes, it's not clear

@bilzebor8457

4 жыл бұрын

@@aedin6397 yes, but what I am wondering is the level of the students. (how many years they spent in college). I thought they were graduate students, but sometimes I have a doubt

@aedin6397

4 жыл бұрын

@@bilzebor8457 I'm sorry, I misread your original question. Very good question you ask -- I've listened to about 1/2 of this Part 2, and (again) it's not clear what the level of students is. Sometimes, of course, it's a mix - grad students and upper-level undergrad. In Dr. Bender's seminal book on Mathematical Physics (co-written with Orszag) was intended for both audiences. But I'm afraid I've not been much help to you :)

1:10:07 1:12:45 Funny eigenvalue problem

at 15:29 i still don't see. D*B is B' +BD but why not just BD like in case of AD ?

@Tyns19

7 жыл бұрын

Tokaji Leo Tokaji Leo hi bro, well it is a notation used in operators algebra the real meaning of it is the following: D(B*y)=D(B) y+ B D(y) It is like dx/dx ( f*g)= f d/dx (g)+ d/dx(f) g

@tokajileo5928

7 жыл бұрын

ok I see now. D is an operator not a function. thanks

@Tyns19

7 жыл бұрын

Tokaji Leo exactly, and it is a first order differential operator, therefore it act in a chain rule on a product of two functions

@mohalq5771

4 жыл бұрын

OK, but why the operator didn't act the same way on a(x)?

@andrewlienhard6758

4 жыл бұрын

@@mohalq5771 because it's AD there. The operator D is not acting on A(x) as it is on the B(x) term, i.e., it's not commutative: AD is not the same as DA.

I dont gey why D*D-1 can be factorized on (D-tanhx)(D+tanhx)

@GordanCable

9 жыл бұрын

D4rckF0x D in this case is the differential operator. The math for operators is a little different then normal algebra. He even says that the factors of operators aren't unique, which wouldn't be the case if your working with just variables.

@macrubit

9 жыл бұрын

D4rckF0x just multiply through and you will see

@2000Finalsky

8 жыл бұрын

+Guillermo Casas multiply through and you will see that it is wrong

@GordanCable

8 жыл бұрын

Again, you have to remember to do the differential operations correctly. The algebra is different, you can't simply foil it out. You have to remember to differentiate your cross terms... remember D(tanhx)+(-tanhx)D /= 0 (D+tanhx)(D−tanhx) =D^2−tanh′x−tanhx⋅D+tanhx⋅D−tanh2x =D^2−(tanh′x+tanh2x) =D^2−(1−tanh2x+tanh2x) =D^2−1.

@jpaultelchannel1702

2 жыл бұрын

(tanhx)(tanhx) = 1 and D.D is obvious. the other terms cancel out.

46:00 i didn't get this part because he didn't consider if Q or a0 don't have a maximum . Am i missing something ?

@chimpluvr5

4 жыл бұрын

I think he is just assuming continuity of Q. Any integral of this type you care to evaluate is over a finite interval, so continuity implies a maximum on this range. A0 is continuous since it is a polynomial.

wich institute or university is this?

@derekflanderschang9654

2 жыл бұрын

Washington University in St Louis (Missouri) - best med school in the nation as well

Humbling

Anybody knowledgeable care to comment on hardness of 2nd order ODE, when it is transposed to 1st order matrix differential eq. Any deep insight why it is not solvable? Wikipedia just says two matricies have to commute.

Ask the person how they knew that 899 is not a prime; they googled it.

There is something which needs to be corrected here, the factorization of y''-y=0 is (D + th)o(D-th)oy=0 and not (D - th)o(D+th)oy=0

is this graduate level or not yet?

There are a couple of really ill-mannered students who were giggling and laughing constantly. Hard to believe they are graduate students!

Is this a phD Lecture? what institute is that?

@crazyengineer101

9 жыл бұрын

seriously? junior learning about quantum physics? that's nice!

@MrDpsc

9 жыл бұрын

crazyengineer101 isn't that standard?

@crazyengineer101

9 жыл бұрын

MrDpsc not that I aware of...

@evanurena8868

9 жыл бұрын

Andrew Chute My goodness. I feel the exact same way you do. When I was young, my dream was to be a mathematician and high school does a shitty job preparing you for college and the real world. How is a repetitive course in American History going to help me become a mathematician. All that time in high school, I could be taking classes like this. You know, stuff that a mathematician actually needs. The American education system just keeps getting lazier and lazier when it comes to meeting the real world needs of kids and when high school kids graduate, they have no skills at all to help with their dream passion because the politicians and board of educators are so consumed by a status quo of standardized testing and mandatory subjects, rather than focusing on the perspective of students and what they truly need. The people that should be controlling the K-12 system are professionals in various different fields of education who know what they are doing and parents. That will allow teachers to have more freedom for lesson plans and choosing which topics to teach. To take baby steps, the first we should do is revamp the purpose of high school, as the system set up for high school is mostly at fault more than anything in the K-12 education system.

@isodoublet

9 жыл бұрын

Andrew Chute This is not Wash U, even though that's where Bender teaches. This is a Perimeter Institute series of lectures.

… and Schrodinger Equation is just a Ricatti Equation.

@jpaultelchannel1702

2 жыл бұрын

The Schrodinger equation is NOT the Ricatti Equation.... The substitution transforms the SE-ODE into a Ricatti which can then be solved just like substitutions will change a 2nd deg ODE to a quadratic. Yet 2nd deg ODE's are not 9th grade quadratic equations.

@millamulisha

2 жыл бұрын

@@jpaultelchannel1702 Was saying they’re the same if you make the substitution but thanks for the lecture. 🤣

@jpaultelchannel1702

2 жыл бұрын

@@millamulisha No, they are not the same. That is the point.

@millamulisha

2 жыл бұрын

@@jpaultelchannel1702 You’re interpreting an informal observation I made concerning a punch line of the video lecture, that with the substitution you transform them into each other. Why are you being so pedantic? 😂

@millamulisha

2 жыл бұрын

@@jpaultelchannel1702 It’s like when a mathematician says, “a doughnut is a coffee cup”. They obviously don’t mean they are exactly the same thing but that they can be brought into agreement with each other such that analysis of one yields analysis of the other. It’s just an informal use of the language. 🤓

Who the hell is making all that goddamned noise? So annoying.

Mathematical physics. Existence is mental and mathematical Existence is both mental and mathematical. In platonic physics, the mental is the domain of causal sets. One aspect of Leibniz's Principle of Sufficient Reason that once puzzled me is that according to the principle, things are as they are only because of a sufficient reason. This caused me to ask, "But isn't a Cause Agent required to bring things about ?" Now, I see that a separate Cause Agent is not required, or that Mind itself (the One) is its own cause agent (is self-causing), following a) Having discovered causal set theory en.wikipedia.org/wiki/Causal_sets now used as the basis of a new theory of gravity. b) Having discovered a suggestion that a set owns or "controls" its objects, c) That in Plato-Leibniz, causation is mental , topdown from Plato's One (Mind) d) That there is no separate Cause Agent in Leibniz, not even God, a belief which is backed by Leibniz's denial of God's intervening in the operations of the universe (denying interventionism). e) That the mental, being subjective, in a sense implies that the mental, being First Person Singular, is its own Cause Agent. It is self-causing amd self-organizing. f) Having found that causal set theory, being set theory, has discrete objects as its subjects. This agrees with my discovery that since Plato's One or Mind is timeless and spaceless, time and space and the objects therein must be discrete points (mathematical points). This agrees with the account of causal sets given in en.wikipedia.org/wiki/Causal_sets "The causal sets programme is an approach to quantum gravity. Its founding principle is that spacetime is fundamentally discrete and that the spacetime events are related by a partial order. This partial order has the physical meaning of the causality relations between spacetime events. The programme is based on a theorem[1] by David Malament that states that if there is a bijective map between two past and future distinguishing spacetimes that preserves their causal structure then the map is a conformal isomorphism. The conformal factor that is left undetermined is related to the volume of regions in the spacetime. This volume factor can be recovered by specifying a volume element for each spacetime point. The volume of a spacetime region could then be found by counting the number of points in that region. Causal sets was initiated by Rafael Sorkin who continues to be the main proponent of the programme. He has coined the slogan "Order + Number = Geometry" to characterise the above argument. The programme provides a theory in which spacetime is fundamentally discrete while retaining local Lorentz invariance." Dr. Roger B Clough NIST (retired, 2000). See my Leibniz site: rclough@verizon.academia.edu/RogerClough For personal messages use rclough@verizon.net

Akne 🤣

capo este viejo qlao

@xHardcorexism

7 жыл бұрын

la cago ctm

who tf is eating

Not a single black student to be seen Not surprising

Mire ha mi expongo lo sigiente despues de ADAPTARLO al dia de Almanake o Calendaio kien es claro para jusgar a las persona de un misterio o paradoja univesal cuando somos en nuesto mundo no inporta festivo ni lluvioso no descano permanente dia noche caranba como es eso

Mire ha mi y tengo halgo ke exponer sobre Hoyente a distansia local Juakin. es conponente X el mujer ke vive tanbien es X entose en el covivensia no se separan claro trabajo en casa y el restante x no me dise yo soy asta caerse pero yo le hago un trabajo y se ponen caotico mente sin descanso o diosincrasia todos como patitos ADELANTE si decaerse (xe lindo eso )anadir al Calendario dia por dia sin falta ningua Espanol

accept the Lord Jesus Christ who has not accepted yet because He is coming back ... sanctify more and more inside and outside ... doing works worthy of repentance and leaving worldliness ... leaving the vanities the tinctures, earrings, makeup, enamels , the fashions of hair and clothes, the short and tight clothes because the Lord is Holy and we must be holy in all our way of living "1 Peter 1: 15,16"