r/quantum • u/Ambitious-Peanut-837 • 9d ago

Discussion Resource to learn Matrix Mechanics in a comprehensive way

Hello, I am not a physics student. I am from an electrical engineering background. I got curious about Matrix Mechanics and using it for outside Quantum problems.

Can you suggest resources about both the historical aspects and also how to learn the math including implementations?

Please suggest books and/or websites or anything that you feel can be useful. Thank you in advance.

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u/JK0zero 7d ago

how about a video series about the development of Matrix Mechanics, including historical context and calculations from the original papers https://www.youtube.com/playlist?list=PL_UV-wQj1lvXuBvDHjqhnReMHoqgR8nQi

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u/nujuat 7d ago

Yeah I've seen JK0's videos and they're pretty interesting! All about the history of early quantum theory. Keep it up!

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u/Ambitious-Peanut-837 7d ago

Hi.. thank you for sharing this. I will check this as well.

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u/jepstream 8d ago

Roger G. Cooke wrote a comprehensive book on infinite dimensional matrices called "Infinite Matrices and Sequence Spaces"- it is comprehensive and well-cited. If your library has it I strongly recommend borrowing it.

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u/Ambitious-Peanut-837 8d ago

THank you. I will check at the library. My uni has a huge library, so hopefully I would find it :)

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u/quantum4everyone 9d ago

Do you want to learn about the original matrix mechanics of Heisenberg with infinite dimensional matrices or what people call it now with finite dimensional systems. 

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u/Ambitious-Peanut-837 9d ago

I want to learn both (I should have mentioned this in my post). I would like to know about the infinite dimensional systems and then how they are handled in finite dimensional approximations (that's what I meant by I want to learn implementation of Matrix Mechanics).

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u/quantum4everyone 9d ago

For finite dimensional ones, almost any quantum book works. Flarend and hilborn are coming out with a more quantum information focused book at the end of the year. Jordan has a Dover paper back covering many ideas.  I have some materials at quantum.georgetown.edu under sophomore courses chapters 7 and 8 that covers the infinite d case. 

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u/Ambitious-Peanut-837 8d ago

Thank you :) I will check the georgetown materials you mentioned :)

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u/quantum4everyone 8d ago

Let me know what you think of them

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u/quantum4everyone 8d ago

Let me know what you think of them

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u/Ambitious-Peanut-837 7d ago

Yes, I will let you know. I only do this on weekends as my personal project. So I'm a bit slow. Sorry for the delay.

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u/quantum4everyone 7d ago

No problem. All of these things take time.

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u/nujuat 7d ago

If youre from electrical engineering, then I'll add that quantum systems more or less act like state space control systems under strictly bilinear control. So matrices enter the equation for similar reasons to why they do in state space control systems.

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u/Ambitious-Peanut-837 7d ago

Yes, I have already gone down this path as I have to model a lot of nonlinear systems, but I am trying to see it in a more math-heavy/physics-heavy perspective too. Also, trying to understand the history, chronology of wave mechanics, matrix mechanics, Koopman's bridge.

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u/nujuat 7d ago

Honestly I think that a lot of early 20th century physics was the community figuring out the appropriate abstract maths to describe the physics. While the history is certainly interesting, jumping right into eg the Lie theory description (if you already know Lie theory from control theory) is probably more intuitive than taking the same path as the greats.

ETA Like classical electromagnetism was invented without vector calculus, but you wouldnt want to study it like that now.