Quantum Sense
Quantum Sense
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What does the second derivative actually do in math and physics?
Happy Quantum Day! :) In this video we discover how we can understand the second derivative geometrically, and we derive a few physical relations using this intuition.
Link to the HQI Blog and their Quantum Shorts Contest: www.hqi-blog.com/contest
Derivation of Laplacian equal to average over sphere in 3D: isis2.cc.oberlin.edu/physics/dstyer/Electrodynamics/Laplacian.pdf
Animations:
All animations created by me within Python, using Manim. To learn more about Manim and to support the community, visit here:
Link: www.manim.community/
Music:
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♪ Intro by HOME
Link : midwestcollective.bandcamp.com/track/intro
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Переглядів: 294 493

Відео

Ch 14: Where does the momentum operator come from? | Maths of Quantum Mechanics
Переглядів 34 тис.10 місяців тому
Hello! This is the fourteenth chapter in my series "Maths of Quantum Mechanics." In this episode, we'll take a look at where the momentum operator really comes from, and we'll discuss how all observables follow a pattern that not many textbooks show. We'll then finish up by showing what the Schrodinger equation looks like in the position, momentum, and energy bases. If you have any questions or...
Ch 13: Where does the Schrödinger equation come from? | Maths of Quantum Mechanics
Переглядів 44 тис.Рік тому
Hello! This is the thirteenth chapter in my series "Maths of Quantum Mechanics." In this episode, we'll finally understand where the Schrödinger equation comes from. We'll first derive that time evolution must be unitary, then use that to get to the form of the equation. We'll then use the fact that energy is the generator of time evolution to take it all the way home (after fixing the units). ...
Ch 12: What are generators in classical mechanics? | Maths of Quantum Mechanics
Переглядів 33 тис.Рік тому
Hello! This is the twelfth chapter in my series "Maths of Quantum Mechanics." In this episode, we'll take a detour into classical physics to learn about generators in the Lagrangian framework. We'll see that each physical quantity generates a change in the state of our particle, which will be key in deriving the Schrodinger equation next episode. If you have any questions or comments, shoot me ...
Ch 11: What are unitary operators? | Maths of Quantum Mechanics
Переглядів 31 тис.Рік тому
Hello! This is the eleventh chapter in my series "Maths of Quantum Mechanics." In this episode, we'll define unitary operators and understand how they preserve the inner product. We'll then show how unitary transformations preserve probability in quantum mechanics, and why that makes it an incredibly important class of operators. If you have any questions or comments, shoot me an email at: quan...
Ch 10: What's the commutator and the uncertainty principle? | Maths of Quantum Mechanics
Переглядів 39 тис.Рік тому
Hello! This is the tenth chapter in my series "Maths of Quantum Mechanics." In this episode, we'll define the commutator, and we'll derive how commuting observables share a simultaneous eigenbasis. We'll then dive into how non-commutation necessarily leads to uncertainty relations in quantum mechanics. If you have any questions or comments, shoot me an email at: quantumsensechannel@gmail.com Th...
Ch 9: What are Hermitian operators? | Maths of Quantum Mechanics
Переглядів 57 тис.Рік тому
Hello! This is the ninth chapter in my series "Maths of Quantum Mechanics." In this episode, we'll take a look into what Hermitian operators are, and some of their properties. Then, we'll show how we can use our physical intuition to actually derive that physical observables must be Hermitian operators. Mathematics Stack Exchange post proving that a bra is the adjoint of a ket: math.stackexchan...
Ch 8: Why is probability equal to amplitude squared? | Maths of Quantum Mechanics
Переглядів 54 тис.Рік тому
Hello! This is the eighth chapter in my series "Maths of Quantum Mechanics." In this episode, we'll dive into how we calculate probabilities in quantum mechanics. We'll derive the Born rule for calculating probability as amplitude squared, then put together our fundamental framework for how we mathematically model a quantum particle. If you have any questions or comments, shoot me an email at: ...
Ch 7: How are observables operators? | Maths of Quantum Mechanics
Переглядів 47 тис.Рік тому
Hello! This is the seventh chapter in my series "Maths of Quantum Mechanics." In this episode, we'll go over how we represent physical quantities as operators in quantum mechanics. We'll also use our physicist's intuition to derive that observables must have real eigenvalues with an orthonormal eigenbasis. If you have any questions or comments, shoot me an email at: quantumsensechannel@gmail.co...
Ch 6: What are bras and bra-ket notation? | Maths of Quantum Mechanics
Переглядів 76 тис.Рік тому
Hello! This is the sixth chapter in my series "Maths of Quantum Mechanics." In this episode, we'll intuitively understand what the bra is in quantum mechanics, and why we need it. We'll also finally justify the power of bra-ket notation, and its relation to the Riesz representation theorem. If you have any questions or comments, shoot me an email at: quantumsensechannel@gmail.com Thanks! Animat...
Ch 5: What are Dirac deltas and wavefunction inner products? | Maths of Quantum Mechanics
Переглядів 53 тис.Рік тому
Hello! This is the fifth chapter in my series "Maths of Quantum Mechanics." In this episode, we'll dig into what the Dirac delta is and how we should understand it as physicists. We'll then use it to show where the inner product for wavefunctions comes from. If you have any questions or comments, shoot me an email at: quantumsensechannel@gmail.com Thanks! Animations: All animations created by m...
Ch 4: What is an inner product? | Maths of Quantum Mechanics
Переглядів 97 тис.Рік тому
Hello! This is the fourth chapter in my series "Maths of Quantum Mechanics." In this episode, we'll derive some intuition for the inner product, and understand why it is a useful tool in quantum mechanics. If you have any questions or comments, shoot me an email at: quantumsensechannel@gmail.com Thanks! Animations: All animations created by me within Python, using Manim. To learn more about Man...
Ch 3: Why do we need a Hilbert Space? | Maths of Quantum Mechanics
Переглядів 138 тис.Рік тому
Hello! This is the third chapter in my series "Maths of Quantum Mechanics." In this episode, we'll find that infinity brings up a few issues within our quantum framework, and we'll see how a Hilbert space fixes them. If you have any questions or comments, shoot me an email at: quantumsensechannel@gmail.com Thanks! Animations: All animations created by me within Python, using Manim. To learn mor...
Ch 2: What are kets and wavefunctions? | Maths of Quantum Mechanics
Переглядів 103 тис.Рік тому
Hello! This is the second chapter in my series "Maths of Quantum Mechanics." In this episode, we'll go over how particles are represented by vectors (aka kets) and how wavefunctions relate to the linear algebraic framework. If you have any questions or comments, shoot me an email at: quantumsensechannel@gmail.com Thanks! Animations: All animations created by me within Python, using Manim. To le...
Ch 1: Why linear algebra? | Maths of Quantum Mechanics
Переглядів 203 тис.Рік тому
Hello! This is the first chapter in my series "Maths of Quantum Mechanics." In this episode, we'll go over why we should use linear algebra as the starting point for all quantum mechanics. If you have any questions or comments, shoot me an email at: quantumsensechannel@gmail.com Thanks! 3Blue1Brown's "Essence of Linear Algebra": Link: ua-cam.com/video/fNk_zzaMoSs/v-deo.html Animations: All anim...

КОМЕНТАРІ

  • @knew_789
    @knew_789 Годину тому

    From Griffiths' Electrodynamics

  • @dougr.2398
    @dougr.2398 21 годину тому

    It is the REAL meaning of inflection ( not watched as yet…. But looks promising )

  • @piyushkaushik4154
    @piyushkaushik4154 21 годину тому

    Bro . Although this is a channel for quantum maths but pls do cover such micro but nuanced and important topics of math as well . Like topics of calculus - I think concept of limits and meaning of it's formulas is part of an abstract section of mathematics (at earlier levels of maths ofcourse. otherwise higher theoretical maths is nothing but abstract). Take up other such concepts from calculus , complex numbers like topics . Great video ofcourse. Subscribed ur channel . Cheers. 🎉🎉

  • @yuminti3368
    @yuminti3368 22 години тому

    I still find it hard to twist my mind around vector space is just describing patern because in my mind I see vector as arrows. It would be great if you could show me an example of vector space made by a different set of object! Very please!

  • @alfredforbessealy524
    @alfredforbessealy524 22 години тому

    well this is... beyond me. At least the intro gave me a different understanding of the first derivative. Guess I'll be back in a few years once I have a handle on that taylor bullshit

  • @adamsmith275
    @adamsmith275 День тому

    0:45 ... 2:05 ... 2:30 ..."INTUITIVE"... Are you sure?... Why do you spend all your time... EXPLAINING... it... REASONING... it?... INTUITIVE... has become a PEST!... I GAVE UP!...

  • @firstnamenonapplicable5138
    @firstnamenonapplicable5138 День тому

    I love when the math I've been srruggling with has unexpected ties with the science I'm getting a foothold in

  • @thibautklinger5178
    @thibautklinger5178 День тому

    How would the Momentum based SE Look If WE Had a 1/x Potential?

  • @Luca-jy2rg
    @Luca-jy2rg День тому

    The best quantum theory series!

  • @kasperborup8683
    @kasperborup8683 День тому

    This is an awesome video! Thanks for making these! However, there is one fundamental part that I don't seem to understand, and I was hoping somebody could help me: That is the relation to the ball for 2D: We look at the 2nd derivative at x0, with f_around calculated based on x0 minus dx and x0 plus dx. That all makes sense to me, but that is not necessarily a circle centered on x0 (as pr the illustration at time 4:35). So how does the circle become a part of this? Grateful for any help.

  • @algorithminc.8850
    @algorithminc.8850 День тому

    Nice coverage of topic. Thanks. Subscribed. Cheers

  • @johnxina650
    @johnxina650 День тому

    at the end bro planted us a bug in the head and left the chat

  • @Mantaw_Agri
    @Mantaw_Agri День тому

    As an Economist my only thought!! To set a Necessary condition for Maximum or minimum

  • @leventegyorgydeak1300
    @leventegyorgydeak1300 2 дні тому

    10:13 - There is something I havent understood for a long time here. psi is in position representation, right? Here you just turn the position wave function into a "continuous vector". However psi can also be expressed in terms of momentum, then it would be |psi> = integral(c(p)*|p>) right? but that means that |psi> = integral(psi(x)*|x>) = integral(c(p)*|p>) which I am pretty sure is not true. Do those psi-s then represent a different hilbert space element, and it is just poor notation that we use the same letters for them? Can someone please explain?

  • @mdsameeransari6691
    @mdsameeransari6691 2 дні тому

    square of dx is (dx)^2 or dx^2 please clarify

  • @kichelmoon6365
    @kichelmoon6365 2 дні тому

    These videos are just so well made and memorable, I love it

  • @kichelmoon6365
    @kichelmoon6365 2 дні тому

    Bae: Come over Me: can't- I'm an arbitrary vector in an N-dimensional Hilbert space Bae: I'm a linear self-adjoint operator A on If, thus my eigenvectors form a basis meaning that every vector in can be expressed uniquely as a linear combination of my cigenvectors: ln) Aln) =AyIn). Me: :-) -) )

  • @supernovap.c.-jk
    @supernovap.c.-jk 2 дні тому

    O my Allah,,,what an explanation! Thank you brother for your hard work. the people who represents physics in a meaningful way, i respect. May Allah grant you.

  • @mintusaren895
    @mintusaren895 2 дні тому

    Smallest to small bigest to biger

  • @ferdaousmasmoudi8216
    @ferdaousmasmoudi8216 2 дні тому

    Thank you a lot

  • @prathameshpatil0810
    @prathameshpatil0810 3 дні тому

    Great Video! Appreciate the effort you take in explaining all these things to enthusiasts! Must have been a lot of effort in the editing as well, Could you please tell me which tool/platform do you use to edit videos like these with equations and numbers flowing around the screen? I would love to create something similar very soon!

  • @user-oy3zf9ce9o
    @user-oy3zf9ce9o 3 дні тому

    Is there similar channel devoted to GTR?

  • @mn-lc7em
    @mn-lc7em 3 дні тому

    Ancient greeks have used intuition and reasons If you know space ecuation, the first der is speed and second is acceleration. So second der is the dynamic of the function. Your demionstration is excelent model. Cong.

  • @aroundandround
    @aroundandround 3 дні тому

    Misleading title: the video does not actually define bra and ket notation like the title implies.

  • @iron_blood7
    @iron_blood7 4 дні тому

    12:58 can someone explain how the chain rule is applied here?

    • @ChrisK-ef8np
      @ChrisK-ef8np 3 дні тому

      chain rule: ( f(g(x)) )' = f'(g(x) * g'(x). You can see f'(...) at the left and the right part is the derivative of the square root with respect to c, which is g'(x) in this case. He applied the chain rule twice, the second time being to find the derivative of √(k^2-c^2), but he just wrote the result, if you need the full steps there are derivative calculators on the internet for free that show the steps too.

    • @iron_blood7
      @iron_blood7 3 дні тому

      I'll check that out, thanks! ​@@ChrisK-ef8np

  • @mzg147
    @mzg147 4 дні тому

    Loved the video! You are really an amazing presenter. One thing that I *will* bite the bullet for is calling Laplacian *the real* second derivative in 3 dimensions. The full second derivative is really a bilinear form, also represented as the 3x3 matrix (hessian) of all possible second order partial derivatives, which the laplacian is just the trace of. There are other second order differential operators that you could get from it.

  • @Anamikaaaa
    @Anamikaaaa 5 днів тому

    Great initiative. Very niche approach .thank you so much

  • @kevinhardy8997
    @kevinhardy8997 5 днів тому

    Tells concave up or down.

  • @damirrakhmanov3119
    @damirrakhmanov3119 5 днів тому

    technically, there is an error on 1:07 in taylor series formula

  • @stefanopogany3767
    @stefanopogany3767 6 днів тому

    What would happen if the time evolution operator were NOT unitary? 0:04

  • @warguy6474
    @warguy6474 6 днів тому

    5:30 "now I'm gonna divide by dx^2" bruh.

  • @MoguMogu818
    @MoguMogu818 6 днів тому

    Watching this as if I didn't get a 52 on my Series and sequences exam.

  • @pandiest7764
    @pandiest7764 7 днів тому

    i am starting my first semester at university at UCSC, and am looking forward to my physics major. thanks for uploading this playlist for me to look forward to viewing the first time, not knowing much of anything, so i can come back in the future and laugh at how much i didnt know.

  • @user-nc2ur9pp6l
    @user-nc2ur9pp6l 8 днів тому

    Imagine waisting time to study these simplified QM mathematical course, i'd better bay some actual textbooks and learn it properly. I was looking for some compitent popular explanation by words, I believe it is pretty possible, not for nonsense like this

  • @skippdiddly1409
    @skippdiddly1409 8 днів тому

    Wow. I'm not so good with math yet this is insightful. Kudos

  • @NormanWasHere452
    @NormanWasHere452 9 днів тому

    This is such a great video, can't believe I've never looked at the second derivative like this. I'll definitely go and watch your series on quantum!

  • @user-zh9zl1zo2u
    @user-zh9zl1zo2u 10 днів тому

    진짜 영상 말도 안되게 잘 만드셨네요!!! wow

  • @modernsolutions6631
    @modernsolutions6631 10 днів тому

    6:00 Iff you can take the derivative from both sides, that isn't always possible but often holds in physics.

  • @bobross9332
    @bobross9332 10 днів тому

    I think that Feynmann was talking about the Cauchy integral theorem. He stated he didn't need to know the center value just the value on the exterior ball.. that is exactly the Cauchy integral theorem -- you average the surface of the ball and you have the center value

  • @CrossMarian00
    @CrossMarian00 13 днів тому

    "nature seems to choose the simplest expressions" *watch in standard model"

  • @riccardoguareschi193
    @riccardoguareschi193 13 днів тому

    Well done. 15’ of great physics

  • @pefactz9.9m3
    @pefactz9.9m3 13 днів тому

    Good❤❤❤❤

  • @SethTheOrigin
    @SethTheOrigin 14 днів тому

    This is an great video. I have a BSc in Mathematics, and I never knew about this

  • @Kounomura
    @Kounomura 14 днів тому

    In fact, all differential quotients of a function are defined by a kind of "curvature". Even the first one shows that the function starts to deviate from the straight line at the given point. The further derivatives give an even more accurate picture of the behavior of the function. Why is the 2nd derivative THE "curvature"? Maybe because the others are negligible from this point of view?

  • @isaiahdebuck4097
    @isaiahdebuck4097 15 днів тому

    Uhhh concavity

  • @andytruong4757
    @andytruong4757 15 днів тому

    0:14 people who know the π joke 👇

  • @danielstump3204
    @danielstump3204 16 днів тому

    it describes acceleration

  • @user-ui5lc3kp7g
    @user-ui5lc3kp7g 17 днів тому

    Please make a same for General Relativity

  • @blisard2648
    @blisard2648 17 днів тому

    mate youve killed this video! Such a complex idea explained so concisely

  • @martinsjardijn
    @martinsjardijn 17 днів тому

    we could consider the brain as a quantum converter following Immanuel Kant's perspective idea