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Thoughts on the mathematics behind quantum mechanics (iusearchlinux.fyi)

submitted 2 years ago by [email protected] to c/[email protected]

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Let me preface this by saying I am not at all well versed in QM, but I've just recently finished a course that took us through most of Griffiths and I have some thoughts.

The thing that blows me away the most about QM isn't necessarily all the standard "weirdness", like tunneling and superposition and whatever, but rather that all of this weirdness can be accurately described by (mostly) pre-existing mathematics. Linear algebra was a growing, but already established field, and the concept of abstract linear vector spaces, and later Hilbert space, came just before and evolved alongside QM.

The fact that we discovered a mathematical language before finding out what that language could describe just blows my mind. I understand this isn't the first time the maths came before the physics, but considering how groundbreaking and unintuitive the theory is I think that fact is quite exceptional. Even more so is that we can use this mathematical formalism to derive physically observable phenomena. I don't know if you get what I mean, but wow. I think that's nuts haha

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[–] [email protected] 2 points 2 years ago (1 children)

Well research is always done off existing foundational theory. But one thing I know about modern physics is people are bad at explaining their work. I remember working through some of a book on statistical mechanics and there was two equation lines directly adjacent to one-another and it took me two and a half pages of work to show how to get there. I will hand it to them, though, it was terse.

[–] [email protected] 1 points 2 years ago

Yeah I've been through a couple of textbooks that do the same. I think Griffiths QM can be pretty egregious in that regard, actually.