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Don't worry about, you're not coming across as rude at all. I guess my point is that you were able to understand the Schrödinger equation without covering a wh

by JBits 4y ago

Don't worry about, you're not coming across as rude at all. I guess my point is that you were able to understand the Schrödinger equation without covering a whole bunch of other stuff first: it's fine to not cover everything. The other conversely is that it's not as simple as checking topics off a checklist: the basics of quantum mechanics can be approached from various perspectives, for example. Personally, I'm keen on gaining a very good intuition of linear algebra — in particular, the idea of writing linear operators as a matrix WRT a given basis and eigenvectors — in order to be confident with the quantum mechanics. I guess you've noticed this though since you've spent time learning something else (the Frobenius method). My overall point is that each topic is very deep and everyone plots their own path through all the different areas. I don't think we're disagreeing. I think really that this is a good list. I suppose that the main thing every beginner wants is a jumping off point which is probably something I've taken for granted. I find university module listing useful myself for computer science despite not having studies it formally.

raydiatian 4y ago
> I guess my point is that you were able to understand the Schrödinger equation without covering a whole bunch of other stuff first I did cover a bunch of other stuff though: 3 semesters of calc, linear algebra, diffeq, classical mechanics & electromagnetism, all before I even studied any of Rayleigh’s experiments. Granted my understanding of Schrödinger wasn’t prereq’d by my understanding of, say, 5/2R solution for the classics ball rolling down a plane and up through a loop no slipping (one of those things you never forget, unfortunately), but like the original derivation Schrödinger did for the wave equation in constant potential field (at least the ones from the textbook I read) goes straight back to Netwon’s F=ma & dp/dt = F for its basis. So you can absolutely bet that my understanding of Newton’s formulation of force was crucial to my understanding of Schrödinger. It was the interplay of linear algebra, complex mathematics, differential equations, and Newtonian intuitions. That is a huge foundation to be building on top of. Furthermore I have done exercises with bras & kets that let you treat the whole thing like a great big matrix, but my experience in building my education has been that if I try to skip a chapter it invariably is a building block that I need to go back and reread. It’s like executing code: eventually, you have to step down inside the function call and execute all its lines before proceeding. And to tie things back around this is precisely why the guy with the website is saying “look, if you want to talk directly to Nobel prize winning physicists, pay your dues, there are no shortcuts.” We’re in a world of climate disaster because we’ve allowed too many shortcutters to drive the boat for too long.

by JBits 4y ago

raydiatian 4y ago

> I guess my point is that you were able to understand the Schrödinger equation without covering a whole bunch of other stuff first I did cover a bunch of other stuff though: 3 semesters of calc, linear algebra, diffeq, classical mechanics & electromagnetism, all before I even studied any of Rayleigh’s experiments. Granted my understanding of Schrödinger wasn’t prereq’d by my understanding of, say, 5/2R solution for the classics ball rolling down a plane and up through a loop no slipping (one of those things you never forget, unfortunately), but like the original derivation Schrödinger did for the wave equation in constant potential field (at least the ones from the textbook I read) goes straight back to Netwon’s F=ma & dp/dt = F for its basis. So you can absolutely bet that my understanding of Newton’s formulation of force was crucial to my understanding of Schrödinger. It was the interplay of linear algebra, complex mathematics, differential equations, and Newtonian intuitions. That is a huge foundation to be building on top of. Furthermore I have done exercises with bras & kets that let you treat the whole thing like a great big matrix, but my experience in building my education has been that if I try to skip a chapter it invariably is a building block that I need to go back and reread. It’s like executing code: eventually, you have to step down inside the function call and execute all its lines before proceeding. And to tie things back around this is precisely why the guy with the website is saying “look, if you want to talk directly to Nobel prize winning physicists, pay your dues, there are no shortcuts.” We’re in a world of climate disaster because we’ve allowed too many shortcutters to drive the boat for too long.