Prof. Schuller is an excellent teacher. Not only is his approach engaging, his dry sense of humor is like little sparkles topping his explanations. This man seems to care deeply that the students understand the topics on which he lectures.
Is he even still alive? It seems like anytime someone leaves a complimentary comment about something on TH-cam the person ends up dead soon after where everybody's just like replying to the existence of a memory of a person and not the real person or something
If you are interested, you can find lecture notes for this course here mathswithphysics.blogspot.com/2016/07/frederic-schullers-lectures-on-quantum.html
Hallo Herr Schuller, ich studiere Mathematik und habe seit kurzem angefangen, Quantum Theory zu lernen. Ihre Vorlesung hat mir super geholfen und ich bedanke mich ganz herzlich für die wunderbare Erklärung!
Sometimes you just find a teacher that is so good that you feel you must watch every little lecture available from them. Fredrik Schuller goes on that list 💜💜💜
I think after a year of reading quantum mechanics, quantum field theory, and quantum information textbooks, I am almost ready to try to follow this course. :-)
In 1:36:03 when he talks about D_A as a proper subset I believe this set should be a subspace of H because otherwise defining a linear map over this set wouldn't make sense.
He said he would have provided some references that treat QM the proper way, but didn't. One such book is Moretti's Spectral Theory and Quantum Mechanics. Heavily recommended if you like Schuller's style.
Thank you very much Dr. Schuller for these (once more) memorable lectures. Crystal clear explanations combined with mathematical rigour and valuable physical insights. I hope you will upload some more lectures in the future.
1:51:40 “The spectrum of an operator lies in the real numbers if and only if the operator is self-adjoint.” This seems to contradict C. M. Bender's 2008 paper Making Sense of Non-Hermitian Hamiltonians. It appears that only the implication “self-adjoint ⇒ real spectrum” holds, not the other way. Or is there something I'm missing?
Take the case of finite dimensional linear algebra, and correspond operators to matrices in some basis. You can take the space of real matrices, correspond them to a subset of the complex operators. There are examples of matrices (even integer components) that are not even symmetric (conjugation leaves them fixed) but have a full spectrum of eigenvalues.
its very satisfying the way he delivers any topic....like even reviewing concepts of classical mechanics( i never looked at classical mechanics the way he explained notion of observables as maps and the two body problem) , i just have one request if anybody ( or even if sir frederic schuller) can give some references for classical mechanics which matches his way of approaching the subject.
"Arnold: Mathematical Methods of Classical Mechanics" is option which gives this presentation of classical mechanics with cotangent bundles. I do disagree with Schuller on his reasoning as to why F(phase space)=I is in interval. Continuity is only one part of it. The other part is is connectedness; if phase space isn't connected, then you can very well have continuous maps to two or more disjoint intervals.
No he's not at all. Γ is the the cotangent bundle of some manifold, that manifold could be a torus or a sphere or whatever. It locally looks like euclidean space but is not euclidean space.
Of course it is... 99% of books introducing to QM are not false. And he is not wrong either. Its a question of settings : here he is going with the more general one (as a mathematician should do). Physics books and teachers tend to avoid all these technicalities. Its a compromise between clarity and rigor. That being said, I like his approach : its not only an introduction to QM but also to non-commutative geometry.
@@sardanapale2302 What do you mean? Why are clarity and rigor mutually exclusive? As a math student, I find that rigor brings clarity to very many things
This method of being very mathematical and rigorous feels very European. Compare with Feynman's approach, and see his talk on "Mathematics vs. Physics", and "Greek vs. Babylonian math". This is going to be a very interesting course, to jump from the "intuitive approach" to the "mathematical approach".
It's very interesting to me as I'm mathematician that just dived into some physics and typical QM courses are unbearable to me - I have big troubles getting into the topic if half the course/book consists of hand-waving pidgin-math style explaining what a Hilbert space is (for a very strange reason, as most Physics students at least in my country have pretty advanced Math lectures before)..
Most QM is taught not with the goal of reaching theoretical physics level, but for the intent of getting a basic understanding to be applied for physical chemistry, materials science, optics, electronics, or other semi-applied part of physics. In those fields, it truly doesn't matter whether wavefunctions are mathematically rigorous or not, as long as they get the job done (and they certainly do). The final arbiter isn't logical consistency but observational evidence. Finally, the biggest challenge in teaching QM is not the math (though it is formidable), but rather it's translating math into claims about reality and vice versa. In that class, everything you learned about classical physics must be revised, and if you must do all that in under a year, good luck fitting the rigors of math in there! Come to think of it, the Feynman criticism of mathematicians-turned-physicists seems to have had a big impact on this "math clouds physics" mentality.
Hi, I think I am not yet prepared quntum theory since I am still learning differential equation and linear algebra. But I listen your lecture while solving differential equation. it helps me concentrate. thanks
I like how he erases the board. He could carry the squeegie with the eraser and save himself some time and footsteps. But what he says while he is cleaning the board is always gold, so in actuality he wastes no time! :)
It seems like in the definition of adjoint, we want the existential quantifier for eta to come before alpha, because otherwise it suggests that there could be a different eta that meets the condition for every alpha. The fact that A* is defined by a single eta gave me this impression. Not sure though; need to keep watching.
I agree that the problem sets and answers would be nice to have, just as MIT does for some of its OCW courses. It would also be nice to have access to videos of what I believe the professor calls the 'problems class' and MIT calls 'recitation', but even MIT provides access to only a few of their OCW courses' recitations.
1:22:00 some defn of a complex hilbert space; 1:33:00 - “where is the notion of manifolds here?”; the field of geometric quantization 1:35:00 linear maps; a densely defined lin map of a vec space - imp for infinite dimensional vector space; 1:39:00 postive linear map; trace-class linear map
2:00:00 so far, axioms are about the kinematics of QM ; now two acioms on the dynamics of QM: how a quantum system develops in time: unitary dynamics ( no measurement happens); projective dynamics (2:04:00) - describes the state right before and after a measurement is made
Electrons velocity dilates time from Einstein's Lorentz, that "quantum gravity" bend in space is exactly equal to the Coulomb force measured with Rydberg.
Thank you. It is a pleasure to see your updates. I was wondering if someone can contact Professor and ask him kindly for written documents, especially for the other lecture "Lectures on Geometrical Anatomy of Theoretical Physics"
not exactly what you are asking for, but I found GEOMETRY, TOPOLOGY AND PHYSICS by MIKIO NAKAHARA has similar contents and notations as the lecture series.
In the video, the professor talks about there being very books on Quantum Mechanics which follow the plan of his course but says he will tell them later. Does anyone know which books he tells later?
Mathematical methods in QM by G. Teschl covers exactly the topics presented in this course, big bonus is, that it is freely available: www.mat.univie.ac.at/~gerald/ftp/book-schroe/
1:01:00 thank God for the indeterminism of QM. It would be boring otherwise. But actually it’s a real fortune that QM has only partial determinism - otherwise nature would have never figured out life.
Randomness and indeterminism are two, very different, things. The quantum randomness and the classical randomness are two, very different, beasts. Most people, even physicists, wrongly confuse the two. My advice, for what its worth, is to keep them separated. The word we experience is not quantum.
In most textbooks, in the measurement postulate tr(rho A) appears (but they treat these as .atrices and mambo jumbo). Is this consistent with Schuller's tr(P_A(E) after rho) order wise? I'm mostly asking to make sure it's not a typo.
Great lectures. One question. Why classical observables cannot have discrete outcomes? For instance, why I cannot ask if a particle is at the left or the right of a given boundary?
The problem is that in QM there are observables whose spectrum lies entirely, or at least partially on a countable set. We do not observe this with classical quantities.
@@LordeRataria Thanks for your answer. How do you define the spectra of a classical observable? I am not sure what do you mean with "We do not observe this with classical quantities.". Why is a question like "is the particle at the left or at the right of the boundary?" not a "valid" classical observable?
@@rayohauno we can define the spectrum of a classical observable as the image of its associated map: recall that we can view an observable *O* as a map O : "Phase Space" --> "Reals". In this way, when you analyse the spectrum of the position observable of some particle (which satisfies Newton's eom), you are simply looking at the image of the map x(t), for instance, to look at the possible values its "x coordinate" can take. If you trajectory allows both positive and negative values for x(t), you can unambiguously determine when it is at "left" or at "right" of the region "x=0", say.
He is saying half (50%) of the observations from the final SG-apparatus are one way and half the other way (50%), the conditional probabilities given that they got through the previous apparatuses.
Damn, such a great set of lectures from an amazing dr. Schuller but no problem sheets. I guess it is not available for us with cheaper tickets. Big thanks for these lectures anyway.
But that is not an observable in the sense of being a function of the cotangent bundle. In this case there is a lack of information about the initial states, so the system is in a mixed state and we deal with ensemble averages
Awesome lecture, boiling QM down to just 5 axioms. One recommendation regarding pronunciation of the English word 'series' which the good prof seems to pronounce in 3 syllables like 'serious'. We native American speakers, however, generally pronounce this word with only 2 syllables. The 'ies' is often pronounced as 'eez'. Also, the accent should be on the first syllable. The word 'series' should be pronounced as "sear'--eez".
Along with Hall's, there is the book 'Quantum Mechanics in Hilbert Space' Eduard Prugovečki and an another book by Valter Moretti 'Fundamental Mathematical Structures of Quantum Theory'.
So far everything good but I want to ask if I need knowledge in topology or he's only going to use hermitian matrices and stuff that linear algebra (college level) can explain. I'll stop the video until someone is kind enough to tell me if I should proceed because I don't know topology (I've taken just one class on real analysis)
He seems to assume familiarity with linear algebra and one dimensional analysis, besides simple topological concepts such as continuity and convergence.
When he talk about the "positive" property of linear maps at th-cam.com/video/GbqA9Xn_iM0/w-d-xo.html, it should be first mentioned that the is a "real" number, otherwise that does not make sense for a general trace-class operator on a "complex" Hilbert space. Note that the states of a quantum system are not required to be "self-adjoint"; so it is not clear that their expectation value, , is always a real number.
I believe it is a graduate level course. (At one point in the series he talks about using stuff from undergraduate courses that the students would have already seen). It should be accessible to undergraduates who have some analysis/linear algebra and topology under there belt. (I'm not sure about the later lectures though as I would assume you need some physics background).
No, he mentions the simple model of spin 1/2 system of QM, which is what I learned in undergrad, is not the correct way. So this series is more advanced.
Anything but didactical: one should first construct the notions one is going to use instead of first using them and then announce one will later explain them. Thanks anyway for uploading.
Perhaps in mathematics, but in physics it is often the other way. Experiment demonstrates an anomaly, in this case a discrete energy spectrum, that the classical formalism does not predict. The axioms are motivated by this observation rather than intuition or some sense that an interesting structure exists above them.
I can't see why teaching mathematics in physis should be different from teaching mathematics in mathematics. Notions should be introduced in due order!
Yes but the due order is different in the two disciplines. I interpreted the introduction as a description of nature as shown through experiment, rather than "using the notions". Like I said, in mathematics axioms lead to structure whereas in physics, structures lead to axioms. It's subjective, but that's just my take on it as someone from a physics background. At the end of the day everyone learns differently.
What are you talking about. Of course it is more didactical to first give the bigger picture and justify the need for understanding the definitions of the components. If you do it the other way around, sure, it is in the "proper" order, but it is not didactical (it would bore the students to death to see countless definitions without knowing that there is an end goal they should care about).
![เป็นไปได้ไหม - WanMai [Official MV]](http://i.ytimg.com/vi/_6lZ6b3_7Vo/mqdefault.jpg)
Prof. Schuller is an excellent teacher. Not only is his approach engaging, his dry sense of humor is like little sparkles topping his explanations. This man seems to care deeply that the students understand the topics on which he lectures.
Is he even still alive? It seems like anytime someone leaves a complimentary comment about something on TH-cam the person ends up dead soon after where everybody's just like replying to the existence of a memory of a person and not the real person or something
If you are interested, you can find lecture notes for this course here
mathswithphysics.blogspot.com/2016/07/frederic-schullers-lectures-on-quantum.html
Thank you, Simon.
Thanks. DO you know the link to part 2 of the course ? Thank you!
Hallo Herr Schuller, ich studiere Mathematik und habe seit kurzem angefangen, Quantum Theory zu lernen. Ihre Vorlesung hat mir super geholfen und ich bedanke mich ganz herzlich für die wunderbare Erklärung!
Sometimes you just find a teacher that is so good that you feel you must watch every little lecture available from them. Fredrik Schuller goes on that list 💜💜💜
I have watched many of his lectures and have never once seen him refer to his notes. Absolutely amazing and what I strive for.
at 48:05 he looks at his notes on the side table, and again at 57:35, for instances
I think after a year of reading quantum mechanics, quantum field theory, and quantum information textbooks, I am almost ready to try to follow this course. :-)
51:40 Finally an advanced quantum lecture series that doesn't assume I am a mathematician. Thanks!
"Nothing is in the artist that isn't in the nan." ---> Nothing is in the teacher that isn't in the man! This guy is a rare avis, a real gem,,,,
Wow!
Now I know what all that measure theory / spectral theory I did in my maths degree is actually used for!
Mathematics starts around 1:12:46
4:03, 14:30, 24:47, 34:46 (wτϕ), 44:10, 46:30, 54:06, 59:29 (cause and effect reversal?), 1:17:07, 1:31:56, 1:37:10, 1:42:40, 1:49:10, 1:55:00, 1:59:45, 2:06:38, 2:08:03
This is great. Now I just REALLY want to see a course on QFT or just QED by Prof. Shuller. Any chance of that happening at some point?
+ANSIcode yes! it would be amazing, such a hard topic explained by a great professor
Yes please !!!!
try osborne, ha has 2 classes on QM and 1 on QFT , VERY DIFFERENT APPROACH tho :)
i'm still waiting :( rip
In 1:36:03 when he talks about D_A as a proper subset I believe this set should be a subspace of H because otherwise defining a linear map over this set wouldn't make sense.
Where are the problem sets? That would be a great supplement to this video series.
are there any updates on these? where can we find the problem sets?
@@johnconrad4439 no but here you can find the lecture notes: drive.google.com/file/d/1I7rIH7Rtm0cCKVuLNeWfFMdKurX123x5/view
He said he would have provided some references that treat QM the proper way, but didn't. One such book is Moretti's Spectral Theory and Quantum Mechanics. Heavily recommended if you like Schuller's style.
Thanks. Can you recommend more books of this style?
Thank you very much Dr. Schuller for these (once more) memorable lectures. Crystal clear explanations combined with mathematical rigour and valuable physical insights. I hope you will upload some more lectures in the future.
1:48:10 I believe your ‘for all’ and ‘exists’ should be switched in order (exists eta comes first)
I concure, you just have to compare with the finite dimensional case.
Thank you very much. It's exactly what I needed in this semester. I shall be grateful to you if you provide the problem sets as well.
Wow I'm so very glad to see this happening! (Another course by Prof. Schuller on youtube and even on a new topic)
1:51:40 “The spectrum of an operator lies in the real numbers if and only if the operator is self-adjoint.”
This seems to contradict C. M. Bender's 2008 paper Making Sense of Non-Hermitian Hamiltonians. It appears that only the implication “self-adjoint ⇒ real spectrum” holds, not the other way. Or is there something I'm missing?
Take the case of finite dimensional linear algebra, and correspond operators to matrices in some basis. You can take the space of real matrices, correspond them to a subset of the complex operators. There are examples of matrices (even integer components) that are not even symmetric (conjugation leaves them fixed) but have a full spectrum of eigenvalues.
watched the whole series, it is hard to find such a clear and precise course in quantum mechanics
How are you doing? Found sth better, something lacking in the course?
its very satisfying the way he delivers any topic....like even reviewing concepts of classical mechanics( i never looked at classical mechanics the way he explained notion of observables as maps and the two body problem) , i just have one request if anybody ( or even if sir frederic schuller) can give some references for classical mechanics which matches his way of approaching the subject.
"Arnold: Mathematical Methods of Classical Mechanics" is option which gives this presentation of classical mechanics with cotangent bundles. I do disagree with Schuller on his reasoning as to why F(phase space)=I is in interval. Continuity is only one part of it. The other part is is connectedness; if phase space isn't connected, then you can very well have continuous maps to two or more disjoint intervals.
Yes, but he's referring to ordinary 4-space there with it's usual topology (which has all the nice properties you take for granted as an undergrad)
No he's not at all. Γ is the the cotangent bundle of some manifold, that manifold could be a torus or a sphere or whatever. It locally looks like euclidean space but is not euclidean space.
Maybe too late to help you out, but Landau & Lifschitz book "classical mechanics" is what you need there.
He has such a classical mechanics course in German: th-cam.com/play/PLyIi3L2232Qo5t61tXfoL6vTW2akFQL-n.html
This lecture changed my entire view on Quantum mechanics, A normalized element of the hilbert space is not the state !!!
Of course it is... 99% of books introducing to QM are not false. And he is not wrong either. Its a question of settings : here he is going with the more general one (as a mathematician should do). Physics books and teachers tend to avoid all these technicalities. Its a compromise between clarity and rigor.
That being said, I like his approach : its not only an introduction to QM but also to non-commutative geometry.
@@sardanapale2302 What do you mean? Why are clarity and rigor mutually exclusive? As a math student, I find that rigor brings clarity to very many things
The best lecture on Quantum mechanics ever. Fredric Schuller should seriously consider writing a book based on his lectures.
I agree.
YESSSSSSS!!!! Finally a new playlist.
Probably the best Quantum Physics intro lecture I've seen. Right to the point.
Thank you so much for uploading a new series of valuable lectures,it really is a good way to study physics with your guidance!
I think you Mr are the greatest physics lector in the world. If you give a lectures on QED and QEF pleas record them. @fredricschuller
This method of being very mathematical and rigorous feels very European.
Compare with Feynman's approach, and see his talk on "Mathematics vs. Physics", and "Greek vs. Babylonian math".
This is going to be a very interesting course, to jump from the "intuitive approach" to the "mathematical approach".
It's very interesting to me as I'm mathematician that just dived into some physics and typical QM courses are unbearable to me - I have big troubles getting into the topic if half the course/book consists of hand-waving pidgin-math style explaining what a Hilbert space is (for a very strange reason, as most Physics students at least in my country have pretty advanced Math lectures before)..
Most QM is taught not with the goal of reaching theoretical physics level, but for the intent of getting a basic understanding to be applied for physical chemistry, materials science, optics, electronics, or other semi-applied part of physics.
In those fields, it truly doesn't matter whether wavefunctions are mathematically rigorous or not, as long as they get the job done (and they certainly do). The final arbiter isn't logical consistency but observational evidence.
Finally, the biggest challenge in teaching QM is not the math (though it is formidable), but rather it's translating math into claims about reality and vice versa. In that class, everything you learned about classical physics must be revised, and if you must do all that in under a year, good luck fitting the rigors of math in there!
Come to think of it, the Feynman criticism of mathematicians-turned-physicists seems to have had a big impact on this "math clouds physics" mentality.
I would suggest you to take a look at Brian C.Hall's book "Quantum Theory for Mathematicians". To me, has been a very enlightening reading.
Thank you very much for your recommendation, I'll surely give it a try.
Hi, I think I am not yet prepared quntum theory since I am still learning differential equation and linear algebra. But I listen your lecture while solving differential equation. it helps me concentrate. thanks
I like how he erases the board. He could carry the squeegie with the eraser and save himself some time and footsteps. But what he says while he is cleaning the board is always gold, so in actuality he wastes no time! :)
This is just amazing. Thank you very much Prof. Schuller for these amazing lectures 🙂☺
It seems like in the definition of adjoint, we want the existential quantifier for eta to come before alpha, because otherwise it suggests that there could be a different eta that meets the condition for every alpha. The fact that A* is defined by a single eta gave me this impression. Not sure though; need to keep watching.
Principle of mathematical analysis by walter rudin
Yes, indeed
Masterful! Are the problem sets available by chance?
I agree that the problem sets and answers would be nice to have, just as MIT
does for some of its OCW courses. It would also be nice to have access to videos
of what I believe the professor calls the 'problems class' and MIT calls
'recitation', but even MIT provides access to only a few of their OCW courses' recitations.
28:00 self-adjunct linear maps as a way to model observables, proerly, for QT
1:13:00 axioms of QM
1:22:00 some defn of a complex hilbert space; 1:33:00 - “where is the notion of manifolds here?”; the field of geometric quantization
1:35:00 linear maps; a densely defined lin map of a vec space - imp for infinite dimensional vector space; 1:39:00 postive linear map; trace-class linear map
1:43:00 axiom2: self-adjointness of a qm observable; defn of self-adjoint map; of adjoint map - 1: 47:00 9 the sutlety lies on this defn)
1:52:30 - axiom3
2:00:00 so far, axioms are about the kinematics of QM
; now two acioms on the dynamics of QM: how a quantum system develops in time: unitary dynamics ( no measurement happens); projective dynamics (2:04:00) - describes the state right before and after a measurement is made
Electrons velocity dilates time from Einstein's Lorentz, that "quantum gravity" bend in space is exactly equal to the Coulomb force measured with Rydberg.
This is not a chemistry lecture, if you are looking for bath salts.
Thank you. It is a pleasure to see your updates. I was wondering if someone can contact Professor and ask him kindly for written documents, especially for the other lecture "Lectures on Geometrical Anatomy of Theoretical Physics"
not exactly what you are asking for, but I found GEOMETRY, TOPOLOGY AND PHYSICS by MIKIO NAKAHARA has similar contents and notations as the lecture series.
Respect, Mr. Schuller.
Thank you so much for uploading!
54:14
You are a very passionate teacher!
In the video, the professor talks about there being very books on Quantum Mechanics which follow the plan of his course but says he will tell them later. Does anyone know which books he tells later?
There are many books following a similar course, look up the one by Brian C. Hall. My favourite one is by Berezin/Shubin.
Mathematical methods in QM by G. Teschl covers exactly the topics presented in this course,
big bonus is, that it is freely available: www.mat.univie.ac.at/~gerald/ftp/book-schroe/
1:01:00 thank God for the indeterminism of QM. It would be boring otherwise. But actually it’s a real fortune that QM has only partial determinism - otherwise nature would have never figured out life.
Randomness and indeterminism are two, very different, things. The quantum randomness and the classical randomness are two, very different, beasts. Most people, even physicists, wrongly confuse the two.
My advice, for what its worth, is to keep them separated. The word we experience is not quantum.
1:51:49 What about the PT-symmetric Hamiltonians?
Amazing Lectures! Wondering if there is a recommended textbook to follow. Thanks
In most textbooks, in the measurement postulate tr(rho A) appears (but they treat these as .atrices and mambo jumbo). Is this consistent with Schuller's tr(P_A(E) after rho) order wise? I'm mostly asking to make sure it's not a typo.
17:40 "hats all over the place" - great!
Great lectures. One question. Why classical observables cannot have discrete outcomes? For instance, why I cannot ask if a particle is at the left or the right of a given boundary?
They can, but their spectra does not lie solely on a discrete set.
The problem is that in QM there are observables whose spectrum lies entirely, or at least partially on a countable set. We do not observe this with classical quantities.
@@LordeRataria Thanks for your answer. How do you define the spectra of a classical observable? I am not sure what do you mean with "We do not observe this with classical quantities.". Why is a question like "is the particle at the left or at the right of the boundary?" not a "valid" classical observable?
@@rayohauno we can define the spectrum of a classical observable as the image of its associated map: recall that we can view an observable *O* as a map O : "Phase Space" --> "Reals".
In this way, when you analyse the spectrum of the position observable of some particle (which satisfies Newton's eom), you are simply looking at the image of the map x(t), for instance, to look at the possible values its "x coordinate" can take. If you trajectory allows both positive and negative values for x(t), you can unambiguously determine when it is at "left" or at "right" of the region "x=0", say.
At 1:27:28 do you mean the set of integers or set of natural numbers ?
at 42:10 ,it should be 25% , 25% in z direction.
He is saying half (50%) of the observations from the final SG-apparatus are one way and half the other way (50%), the conditional probabilities given that they got through the previous apparatuses.
33:55 What was the laugh about??
He writes and says W\tau\phi, which is a clever way to obscure WTF
Looks like a great course. Any chance you could enable TH-cam's automatic subtitles? Thanks!
Does anyone know if there are videos for the other course Prof. Schuller mentions at the outset?
is there any link for the problem sheets and thank you very much for the course
Reference to Wittgenstein's tractatus at @1:06:49 :D
Damn, such a great set of lectures from an amazing dr. Schuller but no problem sheets. I guess it is not available for us with cheaper tickets. Big thanks for these lectures anyway.
sooo good :)
What are the prerequisites I'd need for this course? Or can I start from scratch?
I would highly recommend this video series on functional analysis taught by the great prof Dr.Ole
th-cam.com/video/VXwXkME9uWU/w-d-xo.html
Is this course good for ppl who want to start learning quantum mechanics withoit prior knowledge?
2:27 I can feel marine biologists cringing
sir which book do you follow for lecture delivery.
does this course cover the same topics as a typical undergraduate quantum mechanics?
'Without proof, all become bla bla', by Prof. Schuller
what are the prerequisites?
Could you give me a name of that Textbook Which You Depends on in These Lectures ?
In classical mechanics a coin toss would result in heads or tails. This appears to be a discrete measurement.
But that is not an observable in the sense of being a function of the cotangent bundle. In this case there is a lack of information about the initial states, so the system is in a mixed state and we deal with ensemble averages
Where can I get the problem sheets?
The W\tau\phi standing for WTF is simply w\omega
u\delta\epsilon
ho\phi u \lambda\lambda...
Schuller the boss
Awesome lecture, boiling QM down to just 5 axioms.
One recommendation regarding pronunciation of the English word 'series' which the good prof seems to pronounce in 3 syllables like 'serious'. We native American speakers, however, generally pronounce this word with only 2 syllables. The 'ies' is often pronounced as 'eez'. Also, the accent should be on the first syllable. The word 'series' should be pronounced as "sear'--eez".
What are the prerequisites of this course?
I wish I could access that list of textbooks that develop quantum mechanics in a "mathematically clean way."
Quantum Theory for Mathematicians by Brian C. Hall?
Along with Hall's, there is the book 'Quantum Mechanics in Hilbert Space' Eduard Prugovečki and an another book by Valter Moretti 'Fundamental Mathematical Structures of Quantum Theory'.
Do we have lecture notes for this?
Que aula maravilhosa!
So far everything good but I want to ask if I need knowledge in topology or he's only going to use hermitian matrices and stuff that linear algebra (college level) can explain. I'll stop the video until someone is kind enough to tell me if I should proceed because I don't know topology (I've taken just one class on real analysis)
Btw, I really love that he's fast... I hate slow professors (even though some of them are great)
He seems to assume familiarity with linear algebra and one dimensional analysis, besides simple topological concepts such as continuity and convergence.
When he talk about the "positive" property of linear maps at th-cam.com/video/GbqA9Xn_iM0/w-d-xo.html, it should be first mentioned that the is a "real" number, otherwise that does not make sense for a general trace-class operator on a "complex" Hilbert space. Note that the states of a quantum system are not required to be "self-adjoint"; so it is not clear that their expectation value, , is always a real number.
....round bracket after infity.....ugh..ocd cant stop ignoring ....
Is the trace of A going to be a real number? Why?
Doesn't need to be the case. It is e.g. true if A is positive
why is our universe one where the cauchy property implies convergence like how do we even exist
Ive 😊never believed it
What fukin convergent subsequence??
When someone mentions 'a classical physicist', I wonder where does that guy live!!!
you r so energetic sir : )
34:46 haha! I love it
Is this intended for undergraduates?
I believe it is a graduate level course. (At one point in the series he talks about using stuff from undergraduate courses that the students would have already seen). It should be accessible to undergraduates who have some analysis/linear algebra and topology under there belt. (I'm not sure about the later lectures though as I would assume you need some physics background).
No, he mentions the simple model of spin 1/2 system of QM, which is what I learned in undergrad, is not the correct way. So this series is more advanced.
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“Parallelogram identity”
there's no subtitle?
Why mit quantum mechanics is so little technical and frederic uses so much math?
I think these lectures are not for the beginners of Quantum Mechanics.. he is in a hurry through out the whole lecture..
Anything but didactical: one should first construct the notions one is going to use instead of first using them and then announce one will later explain them. Thanks anyway for uploading.
Perhaps in mathematics, but in physics it is often the other way. Experiment demonstrates an anomaly, in this case a discrete energy spectrum, that the classical formalism does not predict. The axioms are motivated by this observation rather than intuition or some sense that an interesting structure exists above them.
I can't see why teaching mathematics in physis should be different from teaching mathematics in mathematics. Notions should be introduced in due order!
Yes but the due order is different in the two disciplines. I interpreted the introduction as a description of nature as shown through experiment, rather than "using the notions". Like I said, in mathematics axioms lead to structure whereas in physics, structures lead to axioms.
It's subjective, but that's just my take on it as someone from a physics background. At the end of the day everyone learns differently.
@@LaureanoLuna as stated in the lecture, this was in part a motivation to show that it isn't without a reason to learn these concepts.
What are you talking about. Of course it is more didactical to first give the bigger picture and justify the need for understanding the definitions of the components. If you do it the other way around, sure, it is in the "proper" order, but it is not didactical (it would bore the students to death to see countless definitions without knowing that there is an end goal they should care about).