Dirac notation: state space and dual space

📚 State space has an inner product, so it is a Hilbert space. We introduce state space by analogy to a very familiar vector space, the Euclidean 3-dimensional space. We also introduce the dual space, composed of the linear functionals acting on vectors in state space. The whole discussion revolves around Dirac notation, and we introduce kets, bras, and brackets.

⏭️ WHAT NEXT?

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Director and writer: BM
Producer and designer: MC

[the__last__roman]

Excellent video; a very clear exposition of the fundamental mathematics, and concise too. I just wanted to note that I believe there is a small error in the matrix multiplication done at 10:42, and I think it should be c = x_1 x_2 + y_1 y_2 + z_1 z_2 - otherwise, it looked good to me.

[porit]

Thank you so much for this series. The formalism is so beautiful. It was an "aha" moment for me when you talked about the fact that we cannot add a row vector and a column vector together, so that must mean that they belong to two different vector spaces! Mind blowing.

[workerpowernow]

thank you for making these videos. As a current PhD student trying to strengthen my understanding of the mathematical foundations of QM, this series is excellent. For the most part, my experience has been that resources on QM either skirt around dual spaces and the more rigorous aspects of the lin al underpinning QM, or they present the mathematical structure in an opaque manner with little to no motivation. You do a great job of developing the more abstract concepts tied to vector spaces and how they relate to QM in a way that is comprehensible

[supergravity]

Clarity & precision in your presentation is greatly appreciated!

[gingerbrown]

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[El_Abejorro]

Finally I am convinced, as a mathematician, that the bra-ket notation is nice and helpful. Also in general I really appreciate the rigor in your explanations, which is very hard to find in most physics references.Thank you!

[aky]

Dude you are killing it. Great presentation in the entire playlist. And sophisticated enough.

[elenaclaramaria]

I am so very thankful Sir for this series of videos. I am still an undergraduate student and you helped me so so much in understanding key concepts and analogies. I will forever cherish and share these videos. Let this community know if we'll ever be able to support you on patreon, ko-fi or else. Thank you so much!

[rattinyou]

I took (so much as I remember) 4 different courses in quantum mechanics plus an extra two in Q Chem, by far this is THE most comprehensive yet easy to follow narrative I came across! Thank you and genuinely said, well done!

[volkerjung]

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[hidetsuguhiraki]

Through your video series "The postulate of quantum mechanics", I am learning the mathematical model of Quantum Mechanics. Thank you very much for this helpful video series,

[lizard]

You did a much better explanation of this in 17 minutes than my professor has in 2 months! Thank you for relating everything to Euclidean space instead of throwing us into the deep end of abstract nonsense! This was a super helpful summary!😄

[barbaracoelhobraune]

You just saved me! I wasn't understanding a single word of my quantum physics book but then I found you! Keep up the good work, you're helping a lot of slow learners out there (like me haha)

[nomanahmadkhan]

Wow! What an excellent way to teach most abstract things in the least abstract way, great vids.

[HankGussman]

Excellent introduction to QM. I have learnt a bit of General Relativity. And coming to QM afterwards, things line up smoothly with this into.
Many thanks!!

[martonkrenusz]

amazingly intuitive and good introduction to the mathematical foundations of QM, thank you!

[moinakdey]

As I am learning Quantum Computing so these are very useful for me. I love the way you make us understand things. Thanks a lot professor.

[Meow_yj]

I wish I had discovered you earlier; then I wouldn't have failed quantum mechanics :' )
Thank you for these high-quality lectures!

[deroreads]

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[asdfmy]

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