Brilliant. You’ve restricted your scope, stuck to the point, and made a cleaner description of this notation than I’ve seen anywhere else, with visual aids that are minimal and complete. No messin’. Instant sub.
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!!!
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.
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!
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.
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
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?
I like this one more and would like it to be accepted. You can also insert e.g. times-sign (no product sign necessary), or divide by sign or minus sign or any other sign into the square and have a uniform short notation for each operation. Large Sigma and large Pi can be used for other purposes. For example, I use large Pi for pressure.
I was wondering that too. I think explaining it that way was just a precursor to the fact that you need to integrate the continuous wavefunctions to get how much they overlap.
I honestly have never seen this while studying QM, splitting up the wave function point by point into a vector. What I learned during my QM course is that when you have an arbitary wavefunction Psi(x), you can write it as a linear combination of basis functions for the system (similiar to how a position vector in 3D is a linear combination of basis vectors i,j,k : r = a*i + b*j + c*k). Then the corresponding coefficients are put inside the column vector, for example : Psi(x) = A*f(x) + B*g(x) + C*h(x) + ....Then the column vector would be [A B C D ....] transposed. The space can be infinite dimensional so there can be infinitely many coefficients A, B, C, D, E, F, G, H and so on. To me it seems it like this person is trying to force together the idea of the abstract vector |Psi> (which in a chosen basis can be expanded in the form |Psi> = c1 * |1> + c2 * |2> + c3 * |3> + ....., where |n> denotes a basis vector, and it's wavefunction representation Psi(x) = . But I might be completely wrong, my QM knowledge is very minimal.
@@Benjamin-no1vb also ich habe einige deutsche Videos, die ich als Sicherung besaß, auf diesem Kanal hochgeladen: www.youtube.com/@universaldenker_physik ob es weitere Videos auf Deutsch geben wird, kann ich noch nicht sagen
The bra-ket notation is TERRIBLE according to many mathematicians. 1) |ψ> denotes _exactly_ the same mathematical object as ψ, an element of a Hilbert space *H* . So why surround ψ with a "ket" at all?? 2) When λ is an eigenvalue, the notation |λ> is not consistent with the previous one. 3) And, by the way, the notation |λ> is ambiguous cause eigenvectors of eigenvalue λ might not be unique (even up to complex rescaling). 3) A normal notation for the tensor product of φ with the hermitian dual of ψ might just be φψ*, or φ
Who gives a shit about the opinions of mathematicians? The use of bra/ket is in quantum computing, so the only people whose opinions should count are computer scientists.
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Genuinely, this is a brilliant video. A real savior for people wanting an introduction to quantum mechanics.
Brilliant. You’ve restricted your scope, stuck to the point, and made a cleaner description of this notation than I’ve seen anywhere else, with visual aids that are minimal and complete. No messin’. Instant sub.
This is the best explanation I've seen so far! Thank you!
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.
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!!!
Same!!!
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.
Sure I will
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!
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.
thank the lord for this godsend video.
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
Just started reading for my quantum mechanics course next year, this was very helpful!
Great to hear!
Incredibly well explained video!
Superb explanation Sir. You made things so easy in such a simple way.
This video is a godsend. Thank you!
Awesome lecture! Really helped me with notations in quantum mechanics!
Thank you so much， this video give me a clue, and solve my questions to QM for years...
whats up with the weird sum symbol? never seen that ever
Beautiful explanation
Thanks for liking
Super helpful! Thank you!
Brilliantly explained, many thanks
I like very much your explainations! It was very clear and I have learnt a lot. Thank you so much
Thank you Alex, always a pleasure to listen to your lectures ❤
Thank you for the lovely comment, Hertsel!
That's so simple and comprehensive, thank you
Thank you too, for your positive feedback
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?
Thanks...i needed this
You're welcome 😊
This guy is so powerful
Outstanding lecture it is!!! Thanks a lot Sir.
Why use non-traditional sum sign?
I like this one more and would like it to be accepted. You can also insert e.g. times-sign (no product sign necessary), or divide by sign or minus sign or any other sign into the square and have a uniform short notation for each operation. Large Sigma and large Pi can be used for other purposes. For example, I use large Pi for pressure.
What happens when the values of psi(x) and psi(y) are the same? Are they still orthogonal?
Thank you!)
Very nice and useful.
Really nice brief for Bra-Ket Notation - thank you :))
You're very welcome! :)
Great video again, thanks!
Glad you enjoyed it! :)
Really excellent, thank you 🙏
Excellent!!!!!!!!!!!!!!!!!!!!!!!!!
Thanks for the explanation. Could you tell me how to create the animations? What software are you using?
davinci resolve
@@fufaev-alexander for mathematics plots and its animations?
@@magedshaban9680 for animations. for creating illustrations en.universaldenker.org/illustrations
I use adobe illustrator
Do you at all use Manim or will use it in the future?
What do you mean?
@@fufaev-alexander it's 3b1b python library for animations
@@Furetto126 No, I don't use it. But thanks for the suggestion, I'll check it out!
i wish you were my teacher in college
How do we know we can list the x terms if they are uncountable as the function is continuous?
I was wondering that too. I think explaining it that way was just a precursor to the fact that you need to integrate the continuous wavefunctions to get how much they overlap.
I honestly have never seen this while studying QM, splitting up the wave function point by point into a vector.
What I learned during my QM course is that when you have an arbitary wavefunction Psi(x), you can write it as a linear combination of basis functions for the system (similiar to how a position vector in 3D is a linear combination of basis vectors i,j,k : r = a*i + b*j + c*k). Then the corresponding coefficients are put inside the column vector, for example : Psi(x) = A*f(x) + B*g(x) + C*h(x) + ....Then the column vector would be [A B C D ....] transposed. The space can be infinite dimensional so there can be infinitely many coefficients A, B, C, D, E, F, G, H and so on.
To me it seems it like this person is trying to force together the idea of the abstract vector |Psi> (which in a chosen basis can be expanded in the form |Psi> = c1 * |1> + c2 * |2> + c3 * |3> + ....., where |n> denotes a basis vector, and it's wavefunction representation Psi(x) = . But I might be completely wrong, my QM knowledge is very minimal.
Wonderful
BTW, what's that ridiculous notation for a sum at 9:48?? 😂
The usual sum/series symbol Σ works fine for just any structure!
I skipped to this timestamp and audibly laughed out loud at this comment
Tysm
Great vid!
Dude ur my Jesus
3:21 bruh
😅
bruh
it's cool
nice vid! where are your german videos?
Gone :( I accidentally deleted the German channel with another (inactive) channel.
@@fufaev-alexander Oh, das ist schade aber trotzdem sehr gut erklärt. Machen sie weiter ihre Videos sind 🔥🔥🔥
@@fufaev-alexander Planst du die Videos wieder hoch zu laden?
Generell vielen Dank für all die Arbeit die du in deine lehrreichen Videos steckst!
@@Benjamin-no1vb also ich habe einige deutsche Videos, die ich als Sicherung besaß, auf diesem Kanal hochgeladen: www.youtube.com/@universaldenker_physik
ob es weitere Videos auf Deutsch geben wird, kann ich noch nicht sagen
Respect 🫡
nice
Thanks! :)
DÙTÜ🍷🗿😁💯🔥
The bra-ket notation is TERRIBLE according to many mathematicians.
1) |ψ> denotes _exactly_ the same mathematical object as ψ, an element of a Hilbert space *H* . So why surround ψ with a "ket" at all??
2) When λ is an eigenvalue, the notation
|λ> is not consistent with the previous one.
3) And, by the way, the notation |λ> is ambiguous cause eigenvectors of eigenvalue λ might not be unique (even up to complex rescaling).
3) A normal notation for the tensor product of φ with the hermitian dual of ψ might just be φψ*, or φ
Who gives a shit about the opinions of mathematicians? The use of bra/ket is in quantum computing, so the only people whose opinions should count are computer scientists.
Why not use the cat vector in honor of all killed cats in the gruel experiments of Dr. Schrödinger ?😺😿
First
geez.. means nothing unless you do an example.
Work more proofs and theory
skill issue
Horrid echo. You may be talking too close to the microphone.
Value of what? Stupid?. Are we as a races going backwards here or what?
If you can't understand it just say that (or don't) and leave