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!
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.
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.
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.
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.
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!
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.
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.
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 :).
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.
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?
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)
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
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
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.
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
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.
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
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.
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 ?
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
@@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.
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
@@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
@@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 :)
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
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.
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
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.
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.
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
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
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.
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 )
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.
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.
@@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? 😂
@@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. 🤓
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
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"
Can't you tell somebody that loves and breathes their subject? No notes or materials, just straight out of the head. Brilliant man
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.
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 love how his 5 minute explanation of why the ODE is hard turned into like half an hour. 😂
I've them all uploaded. Enjoy!
Thank you!
Thank u guy
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.
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.
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.
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!
ditto he even created order out of the complete chaos of my mind
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.
This prof. is really well prepared for lectures.
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.
I wished I learnt concepts like this in my engineering math classes
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.
i watched this while stoned and felt like a genius
I felt like a genius without being stoned. That's cos he is just SO SO good!
Ya
@@Gebev ya
hats off
The way he perturbatively solved the 2nd-order ODE is exactly the proof of the Picard-Lindelöf theorem...
My mind is blown like never before! Marvellous!
Mistake at 12:00. The minus is in the front on second Tanh(x).
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 :).
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.
Very much like this video！This teacher is fantastic！
Perimeter Scholars International, an MS course program held in partnership with the University of Waterloo
awesome lecture. for once, also a really smart audience in general :)
marvelous! please refer some easily available text for material.
29:22-30:38 The principle of conservation of effort.
We called it the "Conservation of Difficulty" :)
One of my professors called it "Conservation of mathematical ugliness"^^
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?
@Garrett Van Cleef, Lol.... That's a perfect description.
Harsh, but perfect^^
This is actually really good. Even though I'm 15 I could still understand everything he was talking about.
This is a little more interesting than I thought it'd be.
Wow. Great lectures completely marred by the placement of the microphone(s).
Best lectures on mathematical physics
Maybe yes. However, i wasn't able to achieve it online. Please refer to his old book about asymptotic series, if available. ^^
@ 7:24 that is priceless expression from the Prof.
How to find the coefficient of the ground state a(0)=1/2 and phi(0)=e power of -x sq/4 (57:44)
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)
12:13 error (D+tanh(x))(D-tanh(x))y=0
So much ambient noise. Teacher is great!
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
Hi, graduate maths student here. What do you mean by a series of square roots?
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
Where does the closed-form expression at 47:00 for the sequence of integrals come from?
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.
@@waldonumberone thank you - and for anyone else who got confused over why it's 2n - we have n double integrals
I couldn't understand the initial conditions for An (around 41:30)
An(0) = 0
An'(0) = 0
for n>0
can somebody help?
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
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.
He's worth moving to St. Louis for!!!
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
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.
Great content. But 360p?? Really?????
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 ?
at 15:29 i still don't see. D*B is B' +BD but why not just BD like in case of AD ?
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
ok I see now. D is an operator not a function. thanks
Tokaji Leo exactly, and it is a first order differential operator, therefore it act in a chain rule on a product of two functions
OK, but why the operator didn't act the same way on a(x)?
@@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.
does someone know at which university level it was thaught?
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
@@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
@@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 :)
1:08 What about to use \epsilon^2 instead of just \epsilon?
Very intellegect topic welcome to you
Power series combined with green"s function ?
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'?
thank you sir u r a life saver. next generetion education!
Very interesting, thanks a lot!
Wow, this series is enlightening. Much better than Susskind's.
is there a text that goes along with this lecture?
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
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 ?
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.
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
At 3:50, why do we want the z' terms to be 0?
Because we wish for z to satisfy the Schrodinger equation, which has no first-order (z') term.
I dont gey why D*D-1 can be factorized on (D-tanhx)(D+tanhx)
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.
D4rckF0x just multiply through and you will see
+Guillermo Casas multiply through and you will see that it is wrong
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.
(tanhx)(tanhx) = 1 and D.D is obvious. the other terms cancel out.
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
Furthermore how did he derive the parameters for the initial value of the An segment as An=0 and A'n=0?
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
which university is this ??
are there any problem sets to complement these lectures?
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
I own it. There are indeed lots of problems. Caveat: there are no answers.
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.
did the guy at the end ask about new possible lepton?
you can find some of this stuff in his book Advanced mathematical methods for scientists... Watch read... REwatch
In just going to keep on studying.keep studing students.
energy levels are smooth and cont. only in pert. theory with Riemann surfaces, or at all? Probably only the former.
If Feynman had such a blackboard, the infinities wouldn't keeping popping up!!!
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 )
super...
1:10:07 1:12:45 Funny eigenvalue problem
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?
Ask the person how they knew that 899 is not a prime; they googled it.
Is this a phD Lecture? what institute is that?
seriously? junior learning about quantum physics? that's nice!
crazyengineer101 isn't that standard?
MrDpsc not that I aware of...
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.
Andrew Chute This is not Wash U, even though that's where Bender teaches. This is a Perimeter Institute series of lectures.
There are a couple of really ill-mannered students who were giggling and laughing constantly. Hard to believe they are graduate students!
… and Schrodinger Equation is just a Ricatti Equation.
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.
@@jpaultelchannel1702 Was saying they’re the same if you make the substitution but thanks for the lecture. 🤣
@@millamulisha No, they are not the same. That is the point.
@@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? 😂
@@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. 🤓
Ya
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
Gonzalez Steven Williams Cynthia Robinson Nancy
Humbling
who tf is eating
Akne 🤣
capo este viejo qlao
la cago ctm
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
Not a single black student to be seen Not surprising
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"
wich institute or university is this?
Washington University in St Louis (Missouri) - best med school in the nation as well