Ch 1: Why linear algebra? | Maths of Quantum Mechanics

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:
Thanks!

3Blue1Brown's "Essence of Linear Algebra":

Animations:
All animations created by me within Python, using Manim. To learn more about Manim and to support the community, visit here:

Music:
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♪ Astral 7 by Patricia Taxxon
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[alexanderkruszewski]

As a high school physics teacher, I love that content like this is being made which I can share with those students who are hungry for these higher level concepts but are still early on in their mathematical understanding (pre-calculus). Having these clear conceptual bridges with strong essential questions guiding each chapter is both pedagogically sound and a great example of a scientific thinking when walking through the unknown.

[ruben-enjz]

I going to watch all of your videos.

it seems to me that you are the ''3Blue1Brown'' of physiscs :)

please keep making these videos.

[Arnaz]

I love that youtube is learning to recommend good and interesting videos super early now.
This is a great concept with beautiful style, and I'm excited to see the full series! Please keep it up, I hope you get the audience you deserve.

[userant]

Decades ago I took QM but failed to appreciate it 'fully' and have always wanted to return to it. Now retired and with Youtube at hand I'm giving it another try. Thank you Quantum Sense for making it sense and, more importantly, enjoyable. Congratulations, this is brilliant !

[frankzenter]

Proposal for two more chapters:

- What is the tensor product of Hilbert spaces and why does it matter?
- What is the logic of a Hilbert space and why does it matter?

[ajadamd]

as a physics undergrad student, this is one of the best videos i’ve seen on qm and really helps to give an appreciation of the subject

[amoghk.m.]

Quantum mechanics is a subject which I learnt by just blindly accepting a lot of things. While everything seemed more and more consistent the deeper I got into it, in the beginning, it was such an ordeal to feel confident in the subject and know whether I understood stuff right. A lot of times, things didn't make sense. And that feeling lingered for a very long time.
After having gone through all fourteen videos in this series, I think your approach to the subject is really helpful and refreshing!

[alezzi_mm]

There ARE classical properties of physical systems that are discrete. Examples, modes of standing waves, frequencies coupled oscillating objects like molecules.

[alejrandom]

It's amazing that 3b1b's essence of LA is so well made that it sets up a standard for LA intuition

[quantumeveryone]

Thanks for the video. I look forward to the rest of the series. I do have a few comments, and I suspect you know these, but I am of the philosophy that we should teach in a way that we do not have to unteach. The first comment is that the experiment you describe is a quite fictitious one. The closest one could get to the experiment you propose would be to shine light of an energy higher than the ionization potential and then measure the kinetic energy of the emitted electrons and from that infer the bound-state energy. But, of course, each measurement must have a spread to it as the experiment is repeated, because the light shone in will be from a wavepacket so its energy is not well-defined, and unless you have actively excited the atoms, they will all be in the ground state so it won’t show the behavior you desire to use for the example. Second, I believe it is very important to distinguish between abstract vectors and operators and the representation of them as coordinates of vectors and matrices. But here, they are described as the same, or at least could be easily confused as being the same. Finally, the example you give, of an atom, is a classic example that has both discrete bound states and continuum states. But, your presentations sounds like it has only bound states.

[SoundVoltage]

I'm really glad to see your series truly start. Your preview videos were pretty influential in how my own recent videos have been produced. Here's to a long, successful run!

[bernardomarques]

This is awesome!! I'm majoring in physics and I'm super glad youtube recommended me this series so early on. Keep it up!

[meofamily]

Before you got into the argument, I was skeptical of the "good start" you spoke of. Yet, within a few steps, your presentation looked just like a vector. Well done.

[khalidhabib]

i shall remain indebted to u all my life, , i have been waiting for such a course for a decade now.
Thank u very much sir.

[hubertorhant]

Awesome, clear, intuitive, comprehensive. Mapping the physical ontology and the mathematical paradigm attached. Can't wait to build a knowledge of quantum mechanics. 👍

[z.a.s.]

Currently studying Quantum Mechanics at the senior undergraduate level and I am thankful to have stumbled upon this channel!

[frizzarazz]

A very fundamental question, often overlooked by other channels. Well done!

[ToriKo_]

I’m very ignorant, so the leaps I’m making (and the words I am using) are very likely wrong.

But this is the first time I’ve ever seen how the ‘shape/form/description’ of the wave function is just an outcome of us wanting to describe the type of data we get when we try to measure/interact with quantum (quantized) systems. Instead of it being some arbitrarily abstract object sent to us from the heavens. And we can compared to classical systems where we can represent stuff with a continuous function. Thank you for letting me see something about our world for the first time

The assumptions I’m making here are that the ‘linear combination’ of the set values (8:35) is going to turn into a ‘wave function’

One important thing I am still unclear on however, is if the language-based description of a wave function as ‘all the states happening, only after which we get a singular answer’ is an artefact of the mathematics we use to describe the system or an actual transparent view of the underlying physical phenomena

[umairahmad]

Pleased keep continue to teach the concepts of quantum mechanics in easy way
I watched your video firsts time and I loved it.
Usually i don't comment on any video but your fantastic video and your style force me to comment

[yungmaz]

0:42 There is this youtuber I recommend called Parth G who doesn’t just explain the maths of a few concepts of quantum mechanics but also other concepts in physics like Maxwell’s equations