Lecture - 4 Functions in a linear vector space

[@sarthaktiwari3357]

How does he remember all of those things.... Without looking into notes..... He keeps teaching for 1 hour without even having notes or something...... That's why he is legendary teacher

[@nehalamba2747]

after so many years of teaching, its natural to be able to remember all these things. more so if one have amazing conceptual clarity which he have. at his age, almost all prof teach without any book or notes (my observation)

[@antoniomantovani3147]

elementary stuff of vectorr spaces all know this

[@pagalsona]

I watched around 20 lectures of this series and found out that the best book to go with the course is none other than Volume 3 Feynman lectures. Balakrishnan has the mathematical rigor and Feynman has the physical insight. The combination rocks.

[@getaphd]

A piece of advice: Great these lectures are, do NOT try to learn quantum mechanics from these for the first time from these. They are not good at all for that purpose. Watch lectures by allan adams or barton zwiebach for that purpose. These lectures are good for enrichment once you have had a pass through quantum mechanics. 2 years ago, I wasted a lot of time trying to learn the subject from here, but only struggled. Now I have learnt the subject from other sources, and now they are making complete sense and am getting many insights.

[@sdsugermany]

I'm glad these students were unsure about complex variables around 37:00, so that the Professor could go over it.

[@mchammer44444]

This is done to maintain the convention that a vector should have a real non-negative length. For example, consider the vector v = (1, 1, 2i). If you dot it with itself, you get 1*1 + 1*1 + (2i)*(2i) = 1 + 1 - 4 = -2 The length of v is the sqrt of this, which is complex. We want to have lengths of vectors to be real, so that is bad. This problem can be solved by taking the complex conjugate in the bra. This leaves 1*1 + 1*1 + (-2i)*(2i) = 1 + 1 + 4 = 6. The length is now sqrt(6), which is real.

[@rampraveshchaurasiya4737]

Prof Balakrishnan is my an ideal sir....

[@MpazHN]

Greate Lecture! I has been a greate help; As you said, once you get the notations, all the rest comes for free!!

[@captainhampton]

Great lecture, amazing instructor!

[@stoksc]

This is incredible. Really.

[@rosalin8637]

u r just fantastic....sir....ur words get in my mind so direct...and clear

[@maujo2009]

@apoptosis11656 I agree, specially if you use these lectures to follow.

[@stepsvideos]

Excellent lectures. Thanks you!

[@adityadas.mr.cosmos357]

Very nice explanation......very much informative at avery high scale

[@amalenduaman7239]

Where can I find the missing part of this lecture?

[@pavanhanskumar192]

Lecture is really awesome but I have a doubt regarding the expression of bra of psi...... Can someone please explain me why do we introduce complex conjugate of the coefficients while expanding bra psi in basis of bras of phi

[@rambrasil]

yes! great lectures, and available for free!

[@bartholomeosphinx4382]

2:43 - Prof Balakrishnan makes a serious error by claiming that "it is obvious that an L_2(-infty,infty) function must tend to zero as |x| tends to infinity". This is simply not true, as you can have arbitrary tall spikes over an arbitrary small piece of interval. In fact, there exist unbounded functions in L_2(-infty,infty). He then goes on to claim that it even go faster than some power of 1/|x|. Finally he says that there is no requirement that it will be bounded, which is of course a direct contradiction to the beginning of the argument. It is always refreshing to hear Physicists talk about Hilbert spaces.

[@ndmaphy]

Yes, I also think so

[@ochaiogbe1936]

there is a lecture this same prof. Balakrishnan gave where at the first 20 mins of the lecture, he explained why quantum mechanics doesn't appear intuitive to us. he explained that it is because we evolved in the middledimensions. can anyone give me a link to that?

[@banikrai8856]

kzbin.info/www/bejne/ipTQeIybaJ6LfZI

[@rupaligope6716]

where can I get the strting part?

[@anweshachandra8346]

15:00

[@mrunalkamble7176]

Is there any updated version of this lecture where the first 30 seconds are added?

[@independentchannel844]

Mrunal , I also need

[@silenceseeker3544]

same

[@srikanthtupurani6316]

nice lectures. where can i get the notes for these lectures?

[@nirmalghorai8209]

Great lecture 👍

[@anubhabsur8376]

How does one get the inversion formulae, that are mentioned at the end of the video? Could anyone suggest some material to study the same?

[@suryakant6357]

Complex analysis

[@abhishekkawade6494]

What is L2?

[@subrahmanyamsubbu6001]

57:00

[@ambiguity22]

I have a question. How on god's green earth is it possible to learn this kind of math. I'm sitting here watching it, thinking to myself, I haven't the craziest idea of what the hell he is talking about. All theses symbols+words that come out of his mouth in this clipped, cryptic stream of language I can't begin to comprehend.

[@SanchitSrivastavaRnFnR]

He started from quite elementary concepts in lecture 2. Very little prior knowledge of vectors and abstract algebra is required to understand what he's saying.

[@OPify]

I thought I was the only one lost by around 30:00

[@titania174]

Which book should I refer

[@adforfun3675]

The structure and lingo of the lecture suggest that Prof is referring to Principles of Quantum Mechanics by Ramamurti Shankar. But again, a good textbook would go in the same order.

[@zainshah6689]

Hi sir can u send me pdf foam of ur lecturer

[@alexthewombat1]

Haha, He isn't really "teaching" this algebra. He is more just revising it for people who already understand it and just need a reminder. Your very right about the language and symbols. They are the most complicated thing to remember. The maths isn't overly hard. It follows on from High school math but is very confusing because it uses completely different symbols and terminology to high school maths. Its hard to find simple explanations of this stuff but just keep looking. Are u at uni?

[@rambrasil]

Is there something as being "supposed to"? A new kind of racism? Scientific racism? rsss The topic in the lectures is quite nice, but the presentation has been mathematical and operational, assuming some prior knowledge.

[@avishumanray3588]

Of course it needs prior knowledge. It's a Masters level course on Quantum Mechanics. So the prerequisite is ideally 2 semesters of QM in your undergrad, with Dirac notation preferably. Otherwise it's not going to be trivial to keep up with the mathematics.

[@paulhowrang]

@@avishumanray3588 it is not an advanced level course in QM...any elementary/first course book on QM have all this covered..pick anyone. If you really know classical mechanics...have good idea of Matrices.....you are good to go

[@avishumanray3588]

@@paulhowrang As far as I know, this is a quantum mechanics course offered at IIT Madras to M.Sc Physics students. Which is why I said as much. I might be wrong in which case you need to do a bit of legwork on your own before watching this series. However if I'm right, then it is expected that by the time you're sitting for a QM course at MSc level, you will have come across linear algebra and theory of differential equations as you correctly mentioned. Cheers.