Ch 2: What are kets and wavefunctions? | Maths of Quantum Mechanics

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:
Thanks!

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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♪ blinded by Patricia Taxxon
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[pizzarickk]

This series is exactly what I've always been dreaming about. We finally have the 3b1b of quantum mechanics.

[andrewferris]

Man, these are awesome. I passed QM 1 but these videos would have made it so much clearer. I think a video of this style and quality on Local Gauge Symmetries and Forces would be awesome.

[joshdeconcentrated]

These videos are SO incredibly helpful. understanding the concepts better is always a good thing and especially for futureproofing. super underrated channel!

[jamesbentonticer]

I really hope this series does well. A way to conceptualize quantum mechanics could revolutionize how its taught.

[brunofagherazzi]

What an amazing content you're building right here. I've been waiting for this kind of videos for years. Thank you SO much!

[it]

0:00-Recap
0:54-Formal definition of a vector space
2:12-Benefits of vector spaces
2:55-Quantum state as a vector
5:28-Continuous physical quantities (position)
9:35-Wavefunctions as coefficients of ket vectors for continuous list of kets

[blacksmith]

I'v been waiting for something like this a while. The mathematics behind quantum physics always seem to be like understandable math in a language I don't know.

[Miguel_Noether]

I already have QM notions but the way you are presenting this is so good👌

[ToriKo_]

Cool video. Even though I can see that I’m not grasping everything, it’s so appealing how it seems like you’re making it a priority to get us on board with the packaging these ideas come with, helping us to see that actually this is a super natural way of working with these physical phenomena, and helping us feel like we actually *want* these notations.

As small as it was, I got so much joy out of saying “position” out loud as a guess for a continuous quantity, and having that confirmed by you!

One thing I don’t understand is how, 11:13, if we have use a ket to represent *all* the possible information about our particle, then why do have different outcome kets that represent only partial information about our particle, like energy or angular momentum. 11:27. How can we label one |psi> ‘energy’ and another |psi> as ‘angular momentum’, when our ket is supposed to represent *all* the possible information of our particle. Which should cover all information about our particle, like energy, angular momentum, spin, mass etc?

[yenbinh]

As a student who is intensively learning Quantum Mechanics, this video is great!!!! Thanks a lot

[e.s.r]

Amazing video, really clearly explained! Thanks! This is fantastic prereading for my next semester. :)

[pandiest]

as a starting physics major, i enjoy watching videos of all of the higher divisions of physics whilst i'm still in classical physics. it's fun to see what i will be learning later on in my education. thank you!

[johannbrrr]

When we go from a discrete sum to an integral do we have to change the meaning of the coefficients from probability to probability density?

[nablarnermk]

THANKYOU FOR EXISTING, I HAVE MY QUANTUM MECHANICS EXAM IN 2 MONTHS AND A YEAR AGO THIS WASN'T AROUND YET TO HELP!!!! KEEP UP THE EXCITING AND GOOD WORK

[vincentlin]

Thank you so much for saving my quantum mechanics midterm and my life. Best quantum lecture ever.

[roelofvuurboom]

Great explanation. Explanation of why linear algebra in QM is so simple and intuitive. Really cool.

[alexbaify]

Loving this series! Thanks so much for doing this!

[niranjanca]

THE BEST Youtube channel which made me understand the quantum things all the best brother you really should have bright

[cstruble]

Thanks! Just the balance of rigorous and intuitive I need.

[sanderdude]

MAN this series is amazing!
Thank you for putting in the time and effort to make this!