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Spivak (of differential geometry fame) wrote a book with this precise title:

https://archive.org/details/physics-for-mathematicians-mecha...

It's a very interesting take on classical mechanics.

I own a copy of that book, and I also highly recommend it! (The full title is "Physics for Mathematicians: Mechanics I", but sadly we're now never going to get a "Mechanics II".) It has a different goal than my notes --- he's more interested in building up classical mechanics very, very carefully from first principles --- but it's a fun journey if you have the time to spend on it.

As a former physicist, I never understood the full math behind Schrodinger's equation. Since then I ventured into CS, so I wonder if this book will be a good refreshment.

The Schrodinger equation is just restating something you may already know if you studied physics. The Hamiltonian is the generator of time translations.

Look at it again with that understanding in your head: https://en.wikipedia.org/w/index.php?title=Special:MathWikib...

H acting on a state gives you the time translation of the state. That's the crux of it.

Rainer Sachs and H.-H Wu have one about general relativity too. https://link.springer.com/book/10.1007/978-1-4612-9903-5

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