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.