Yes, I know and knew perfectly well that a linear operator separates out the eigenvectors, multiplies each one by a scalar eigenvalue, and puts them back together again. But I thought that was supposed to be physically happening to the wavefunction. Not that it was a math trick developed for extracting the average of the eigenvalues when you took the operated-on wavefunction's dot-product with the pre-operated-on wavefunction.

The quantum physics textbooks I read were happy to define linear operator-ness in great gory detail, but they never actually came out and said, "This is not something physically happening to the wavefunction. We are just using this math trick to extract an average value."

Why would they say it? After all, quantum physics is meaningless. The wavefunction doesn't really exist. All you can do is memorize certain math tricks that make predictions. All the math tricks are on an equal footing; it's not that some are physical and some aren't.

So I would stare at the operators and their definitions, trying to figure out what was physically happening, until finally - I think while looking at the "position operator" - I realized it was a math trick, not an event description.

I haven't felt so indignant since I realized why the area under the curve was the antiderivative, and realized that at least two different calculus textbooks neglected to mention this in favor of elaborate formal definitions.