Understanding Quantum Mechanics #4: It's not so difficult!

In this video I explain the most important and omnipresent ingredients of quantum mechanics: what is the wave-function and how do you calculate with it. Much of what makes quantum mechanics difficult is really not the mathematics. In fact, quantum mechanics is one of the easier theories of physics. The mathematics is mostly just linear algebra: vectors, matrices, linear transformations, and so on. You've learned most of it in school already! However, the math of quantum mechanics looks funny because physicists use a weird notation, called the bra-ket notation. I tell you how this works, what it's good for, and how to calculate with it.

Correction: At 4:44 the left side shouldn't have a square. Sorry about that.

[hesitantjaguar]

I both understand perfectly and am completely clueless at the same time, I must be the Human version of Schrödinger's cat.

[johnathancorgan]

It's amazing how linear algebra underpins quantum mechanics, machine learning, digital signal processing, error correcting codes, computer graphics, and so much else. It's a great example of how learning the underlying math allows one to understand so many seemingly different fields of knowledge. Great video.

[gus]

Finally something at my level! I'm an engineer. The average "laymans" explaination is too layman. The average specialist explanation assumes you spend all your time doing physics - and have read all these books and papers. Thank you.

[cmilkau]

"In quantum mechanics, we only ever observe the shadow of tge wave function" - Woah, Plato was right all along!

[smw]

I actually have a Master degree in Physics from ETH Zürich ( 25 years ago), but had my Professor explained me the basis of QM like this
I would have had much less problems and sleepless nights :-) !
( now in the right videos comments)

[ibji]

I once took my car to a quantum mechanic. As long as I don't look at the speedometer, I can get where I'm going.

[ernobuzas]

Sabine, to me you are the best Physicist on Youtube! The no-nonsense style, concise and clear structure of the episodes and the intellectual rigour and honesty - you’re doing something that, as far as I know, is in very short supply here. Keep up the good work, we need people who have deep understanding and can also explain as clearly as you can!
I love your channel.
Also, I’m not German but I enjoy hearing the correct pronunciation of German names on the Internet.

[jumperclown]

This has very quickly become one of my favorite youtube channels ever.

Concise explanations of scientific theories without climbing aboard the hype train or spending an hour explaining the double slit experiment for the millionth time. Thank you!

On that note, I would love to get your thoughts on the delayed-choice quantum eraser experiment.

[CaptainJeoy]

I think it's official now, Sabine's channel is where you go to fully understand what you've been taught in the university. 🔥

[karlmahlmann]

It's been almost 40 years since I took Quantum. This is a wonderful refresher. Thank you.

[MathScienceClassroom]

Excellent explanation! As a Science teacher myself, I love when someone can break down seemingly incomprehensible concepts into understandble smaller chunks.

[weylguy]

Great introduction, Dr. Bee!. I cannot emphasize the importance of using the Dirac bra-ket notation too much, as it greatly simplifies the mathematics of QM. My favorite elementary text is Sakurai's Modern Quantum Mechanics, whose first three chapters provide everything one needs to know about the notation and its applications.

[adrianmuresan]

I was literally taking a break from reading Sakurai's first chapter and watched this video. Excellent explanation. I appreciate the part on the density matrix, I guess that's where things get really exciting.

[frvo]

This must be the most "not so difficult to understand" difficult to understand video I've ever seen 🤷🏻

[girlygirls]

I am a final year Bsc physics student who was very worried about their understanding of QM, something just didn't click for me. You just summarized everything that needed clearing up for me within 8min, I feel like all the lectures I have witnessed finally made complete sense. I am shocked and honestly a little in love. I never write comments on yt videos but WOW and THANK YOU... THANK YOU SO MUCH.

[GeorgMayer]

this were 8 minutes which answered a lot of questions which i never dared to even try to find out, because I thought I would never even get a clue of what these brackets mean. Thank you so much!

[yvbwzfn]

Whenever I come across a video claiming in its title that "Quantum Mechanics (or any other fancy, popular scientific term) were not so difficult" I find myself thinking about misleading titles and how they are supposed to generate traffic. The explanations in this video, just as in all the other videos on the matter, are neatly arranged versions of standard textbook contents. While I do appreciate the effort that goes into scripting and producing these videos I am always missing an advice of caution. The fact that the mathematical basics of Quantum Mechanics are comparatively simple does not imply anything really, least of all that Quantum Mechanics are not so difficult. The brief glimpses on "vector spaces", "dual spaces", "inner products", etc. provided in this video are merely first steps into a massive subrealm of mathematics. I agree that anyone who is interested in Quantum Mechanics has to work on their mathematical abilities although I highly recommend using these videos as a motivation to acknowledge, rather than to deny, the difficulties of theoretical physics and maths. The net information seldom surpasses party-trick quality standards and that is all well because being too complex to be legitimately summarised in any video (of finite length and information density) is in the nature of things!

[munziroon]

In this video I understood something which I never understood by watching 100rds of videos!!!
Thankyou so much for this simple and powerful explaination!
It would be amazing if you write a book on quantum mechanics, , , hope to see that soon....!!!

[delmothurifera]

This is an amazing video. I am a biologist with a master's in physics: I always had trouble with mathematics but come to realize that it only takes a simple explanation from someone at the correct speed and structure of ideas. Everyone is different. I wished I had seen this video when I started my master's. Thank you, I can't believe how well you explain these concepts!

[sneffeamv]

I think one should make a distinction between the state and the wavefunction. The state is an abstract mathematical object whereas the wavefunction is a complex function of spacial coordinates. If you want to obtain the wavefunction from the state you project it onto your spacial basis.