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.”
I think is is a common problem for many mathematical conventions in physics.
The same thing happened be me in high school physics. I was confused by the torque vector, and I spent an entire year thinking that somehow rotation causes a force perpendicular to the plane of motion. I just could not visualize what the heck was going on.
Finally I realized the direction of the torque vector is an arbitrary convenience. My teacher and textbook both neglected to explain why it works like that.
I think is is a common problem for many mathematical conventions in physics.
The same thing happened be me in high school physics. I was confused by the torque vector, and I spent an entire year thinking that somehow rotation causes a force perpendicular to the plane of motion. I just could not visualize what the heck was going on.
Finally I realized the direction of the torque vector is an arbitrary convenience. My teacher and textbook both neglected to explain why it works like that.
The “why’s” are important!