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 rigour and Feynman has the physical insight. The combination rocks.
I remember these blowing my mind 11 years ago (we had an incredible Quantum Mech prof in Dr. Abhinav Gupta, but we unfortunately couldn’t rewind his lectures).
For those having slight issues with duals, dual of a vector space is the set of all linear forms of the vector space, where a linear form of the space is a mapping of all unique elements of the space to a single element from a set of scalars. Thus the set of all linear forms as in transforms/ mappings is the dual of the vector space. Now since linear transforms can always be represented by vectors or matrices, thus the transpose of a row vector is in itself a linear form of the vector as it maps it to a scalar. Thus sir refers to the transpose as an element of the dual of the linear vector space. Great lecture, I return to freshen memory every now and again, truly a treasure.
Me too!!! But thankfully I could crack railway exam for CMA... You should try such exams too on public sector that asks for physics post graduation or graduation
Very nice explanations by Prof. Balakrishnan. He explains such an abstract concept with a very simple manner without diminishing the substantial contents. Thank you, Professor!
This is a great lecture series to watch along side Leonard Susskind's Quantum mechanics series on the Stanford channel. I wish they'd get the rest of the lectures up soon. Happy New Year!
@AtomosDemocritus Thanks for the info! This is what I am working on the Linear vector space ǀΨ > forms the time line for the object or observer in their own reference frame. The quantum w-particle function is a vector for a moving object increasing its mass and slowing time down.
His son Hari Balakrishnan and daughter hamsa balakrishnan are professors in Computer Science and Aerospace Engineering Departments of MIT. You got believe this guy, he knows the meat pretty well. His wife used to be working in IMSC which is pretty renowned for doing the physics stuff. Have fun and njoy his lectures. He is my guru and now I am in OSU
I find him quite easy to understand. The material itself gets tough, so there's a limit to how easy you can make it. I really like his style of teaching though.
I could not leave the lecture without leaving a comment, which I seldom do. Sir U r genius, fantastic explanation. My favourite proffessor is RAMAKANTH in kakatiya university. Very similar to your lecture sir in almost every way as ur lecture Thank you sir
I do know all the things and all our concepts will turn out wrong if try to push to ultimate consistence......but I can tell all our manufactured physics you are such an amazing mentor for it sir Thank you Sir
Superb - many thanks to Prof. Balakrishnan and IIT. Minor correction though: At 0:27:00 he is wrong when saying that the functional S_psi forms a vector space. It is the set of all S (not just S_psi) that form the dual vector space. The confusion continues for a while, but at 0:31:50 one of the students has spotted the problem and apparently (question is inaudible) asks for a clarification. The answer seems to be wrong at first, but from 00:32:10 to 00:32:25 the statement is correct.
I find prof. Shankar morw fun and fluent in math-physics . He also will make u understand where the formula comes from with physics explanation . He adds variables as he goes with logical explanation along side untill picture completes..
@@janapratimdevgoswami3431 yes super good. But third world countries lag behind because math is tought in abstract form. Math must be tought in such a way its application is demonstrated to studenta. The student will love it. Application of math is what makes students love it .
@@MrAzizisse Actually I found it the opposite of what you said to be true in India. Like here Math is taught only in terms of how to use it in physics or any other stuff there is no basis or relevance to pure abstract math here unlike in western countries
@AtomosDemocritus It does seem fitting somehow, in just the same way we have gravitational time dilation around objects of great mass and we also have time dilation when an object accelerates and mass increases. I think this has more to do with the wave nature of energy and mass than two different types of w-function. Nick
@AtomosDemocritus This is what I was thinking each scalar would be formed by adding the two previous scalars together and if the process was continuous, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ad infinitum?
Question, If we have to add two vectors together to get a new vector don’t we create the Fibonacci sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ad infinitum?
It is very easy as logic but hard as notation. It takes more time as physicist but rather less as mathematician. probably conjugate variables, with optimal uncertainty.
@DanFrederiksen Please investigate the fundamental courses on linear algebra and then observe the lecture. A basic knowledge of fundamental math is assumed in a lecture on quantum physics. Good luck.
Say we are finding the dual space of R^n, take an element in R^n which looks like (x1,x2,....,xn)^t (meaning transpose), somehow we have to find a way of associating another vector to this to produce a scalar. We do this by taking the row vector (y1,y2,...,yn) and multiply to the above vector. In this process i have taken the entire original column vector X as the reference in the vector space and found a dual. The process never requires you to multiply x1 to all y1,y2.. etc.
Don't phi and xi have to live in the same space for the inner product to be defined on a bigger Hilbert Space? Are V and V~ subspaces of a bigger space? Maybe he clarifies this.....patience!
Is it correct to say that the appearance of uncertainty when trying to quantify a canonically conjugate pair of system variables is the intrinsic nature of the mechanism adopted to probe the system?
doubt: In theory while defining bra vector set we said that we take a reference element say φ and apply it on each element vector in the space to produce a scalar such that it satisfies those 2 conditions. How can matrix multiplication be an example of this? In matrix multiplication say we do x1y1+x2y2+...... so we dont apply x1 on all y1,y2,.... and x2 on y1,y2,....
Can any Indian explain if the song is a prayer? Which is its language? What would be its English translation? ??? ??? Besides these, they are really very useful lectures
Karka kasadara is from sacred kural Tamil better than Sanskrit prayer Karka kasadara means learn doubt free and error free.Both for Teacher as well as students it is also universal.Dont worry about Sanskrit slokam none understands in India too.sir Ing Louis Brando Sanskrit is not the mother tongue of anyone in India including Brahmins who uses to chant mantras in temples.
Its the Vedic chant which means ..... Om Saha Naav[au]-Avatu | Saha Nau Bhunaktu | Saha Viiryam Karavaavahai | Tejasvi Naav[au]-Adhiitam-Astu Maa Vidvissaavahai | Om Shaantih Shaantih Shaantih || Meaning: 1: Om, Together may we two Move (in our Studies, the Teacher and the Student), 2: Together may we two Relish (our Studies, the Teacher and the Student), 3: Together may we perform (our Studies) with Vigour (with deep Concentration), 4: May what has been Studied by us be filled with the Brilliance (of Understanding, leading to Knowledge); May it Not give rise to Hostility (due to lack of Understanding), 5: Om Peace, Peace, Peace.
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?
english is the common language of india, everyone comes to these iits from different states, and not everyone understands madras local language, but everyone does understand english :)
sir iam from hp ihave a equation that found that light has dual nature for some time at a point that is called by me indiantrone away from this point light has only partcal nature
Not true. I was kidnapped by Hizballah and held in captivity for several years in the mid 1980's. Every afternoon, a masked man put a gun in my mouth and forced me to watch this video. Ironically, it was the best part of my day. My hat off to you, Professor V. Balakrishnan.
Language is Sanskrit. The literal meaning is: "OM. Let all of us protect each other together, may all of us enjoy together, may all of us work together and let our study become radiant. Let there be no hatred between us, OM Peace, Peace, Peace"
The set of linear maps from a vector space to the field (usually R or C) is also a vector space. This space is called the dual vector space. See here: en.wikipedia.org/wiki/Dual_space
Starting with "an element of the original LVS" (= a column-vector = a ket-vector) you can only produce a SCALAR by multiplying it with "an element of the dual LVS" (= a row-vector = a bra-vector). In other words, a (1xn)-matrix multiplied by an (nx1) = a (1x1-matrix = a scalar. Listen carefully from here: 43:08
