Bra-Ket Notation and How to Use It

00:00 Wave function and Ket vector
03:17 Bra vector
04:35 Scalar product
05:53 Inner product
06:35 Visuals interpretation
06:49 Tensor/outer product
07:42 Projection matrix
08:39 Basis change of kets

Books by Alexander Fufaev:
1) Equations of Physics: Solve EVERY Physics Problem
2) Alexander Fufaev and His Never Ending Story:

[jamesgarrity]

Genuinely, this is a brilliant video. A real savior for people wanting an introduction to quantum mechanics.

[reversalroadmap]

This is the best explanation I've seen so far! Thank you!

[kmunson]

Like other commenters have said, I have seen many video's but yours explains it so clearly with fantastic graphics. So happy to find this channel.

[cavendishcavendish]

Thank you so much for the clear explanation professor, I wish you explain for us all lessons related to quantum mechanics 1 and 2, and the line, surface integrals please.

[physiologic]

Man, thank you so much for this video! I have seen so many explanations but none come close to the kind of intuitive and visual understanding this video has given me. Just got a subscriber. Keep up the good work!!!

[Vagabond-Cosmique]

That was an incredibly clear and beautifully presented explanation. Nice and simple, while also being comprehensive. I don't think I've ever seen such a well made and thorough explanation of the mathematics of quantum mechanics that's also easily understandable and easy to follow for laymen.

Thank you and well done ; Paul Dirac would be proud!

[grad_student]

thank the lord for this godsend video.

[mikeperri]

Thank you Alexander F - I've struggled to understand other explanations of bras and kets. Yours is clear and simple. Pity others don't adopt the same care for their readers and listeners.

[teikono]

Just started reading for my quantum mechanics course next year, this was very helpful!

[nmrenyi]

Awesome lecture! Really helped me with notations in quantum mechanics!

[Proudindian]

Superb explanation Sir. You made things so easy in such a simple way.

[giorgosg]

That's so simple and comprehensive, thank you

[davidhuo]

Thank you so much， this video give me a clue, and solve my questions to QM for years...

[hertselcorech]

Thank you Alex, always a pleasure to listen to your lectures ❤

[dumebidonald]

Excellent tutorial.
I have an opinion that in solving the equation in 8:07, the scalar product should be treated first because I feel it more logical & maths because of the brac & ket notation applicability. We still get same answer

[mathiscuisinaud]

I like very much your explainations! It was very clear and I have learnt a lot. Thank you so much <3

[samsunnahar]

Outstanding lecture it is!!! Thanks a lot Sir.

[picosoft]

Really nice brief for Bra-Ket Notation - thank you :))

[lamontcranston]

Thanks for this video. I'm just an old guy trying to learn new tricks and the introductory portion confuses me. The initial 2-D plot is fine, but when you speak about a point or value in the Hilbert space, the value of any point is psi(x, y, z, ... or as many dimensions as you have). Using psi(x1) and psi(x2) (to me) only describes the x1 component of psi at x1. Wouldn't it be better to use a different letter such as Q, as in psi(Q1) where Q1 is a matrix of x1, y1 and z1?

[vincentlanglo]

What happens when the values of psi(x) and psi(y) are the same? Are they still orthogonal?