> One does not deduce them like one do in math. The physicists who actually did this stuff apparently knew this, and considered the math more akin to toying with the models to see what happens, to see if they could get better models
Which is absolutely true. Part of the problem with quantum mechanics texts is that they're almost all descended from Oppenheimer's lectures (via Schiff's book) to graduate students who already knew this, and just needed someone to brain dump the latest techniques.
But then it's mixed with really basic misunderstandings, like
> Many physicists like to believe that this makes the underlying model irrelevant; that the matrix behaviour, its eigenvalues, is the only thing that matter. You will encounter lots of this in books about Quantum Mechanics. This however is not science, because it ignores Ockhams Razor; the models shall be the simplest ones. A sparse matrix is simpler than when it is Fourier transformed, or put into atom orbitals. (I thank Eliezer Yudkowski who gave a reminder that Ockhams razor belongs here too.)
Quoting Eliezer Yudkowski is a useful heuristic for not taking someone seriously, but this quote implies that the author missed the whole point of linear algebra. And is falling into the traps described by Theorem IV in van Kampen's [Ten Theorems about Quantum Mechanical Measurements](http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=617...).