Ch 11: What are unitary operators? | Maths of Quantum Mechanics

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:
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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♪ Surf (feat. VIQ) by Division Street
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[aafeer]

If you make a PDF I will buy it, and probably I will not be the only one. This really associates the formal math and the intuition in a striking way. Well designed, brilliant accomplishment.

[NikhilGupta-hvui]

This is amazing content! You have reminded me back of the time when 3b1b used to post his series on calculus and linear algebra. This is just awesome. What books would recommend me to follow along with this and self study quantum mechanics ?

[nikolozchaduneli]

Loving the series, excited for the upcoming episodes!

[UniverseForme]

I recommend the people who are all beginners for quantum mechanics before watching the video try to read QCQI by Nielsen & Chuang. It might improve your understanding. Thanks for the series Sir.

[NumbToons]

Your videos are the ones which I will be coming back to see again and again, in present and future.

[nicco-sixty]

Have you covered why we need complex numbers?

[lingling]

Thank you for making this video and saving me from the hell of math This video is amazing, so clear, so understandable.

[toomaray]

amazing series, keep it up and hope you continue with the amazing content!

[opubogbenebo]

The presentations have been quite educational, admittedly. Yet the Unitary Operators concept found immediate applications in several projects currently engaged upon.

[jmostei]

Amazing series! Very good job. Please continue doing this.

[ytsubhrajyoti]

The content is really good. Can I use parts of these clips in my educational videos in my regional language?

[khiemgom]

I still finds it weird that there could be orthogonal eigenbasis. Like isnt that mean the operator is just scaling the probability of their definite states?

[danceordrink]

Hello, I like your videos for they're reasonable and convincing. I have problem understanding why the general unitary gate in quantum computing has 3 angles to write into. I don't understand what it means. Could you explain it? Thank you.

[VenusianJungles]

I think your definition of a unitary operator at 1:46 is incorrect, this is the formula for a Hermitian operator, a unitary operator is where U*=U^{-1}. If I am wrong please correct me I am here to learn.

[Yashlessgoo]

why is left slot of the inner product antilinear?

[AdnanKhan-mmbo]

Which software you're using to make that videos..??

[donizetenunes]

Tenho uma duvida: A matriz do operador unitário somente possui valores diferente de zero em sua diagonal principal e estes valores serão sempre iguais a 1? Como construir este operador a partir de um Ket?

[dr.robotnik]

It all makes sense now, that is " Quantum Sense" HA😆.

[TheWyrdSmythe]

I think there’s an interesting question about whether unitarity is _always_ preserved. It’s considered bedrock in standard QM, but I wonder if when we finally include gravity we’ll find there are exceptions. (And, if so, perhaps that solves the BH information paradox.)

[alessandroc.]

And yes, six hours ago, i probably failed my quantum mechanics exam🙂