When to Choose Between Operators for Theoretical Calculations in Experiments?

[nonequilibrium]

Hello,

When an experimentator knows his set-up, how does he know which operator to use (if he were to do theoretical calculations for prediction)? Is the distinction always clear? E.g.: is the distinction between a position and a momentum measurement apparatus always clear? I can imagine an experimentator using a time-of-flight measurement to measure momentum, but the measurement itself is for position, so can the experimentator choose which operator he uses (of the two)?
On the other hand, if the distinction is always clear (in which case--correct me if I'm wrong--time-of-flight measurements are not "allowed"), can you name a "pure" impulse measurement?

 

[DrClaude]

It is a question of analyzing the experiment and figuring out what it is actually measuring.

For instance, in the original Stern-Gerlach experiment, they actually measured the position of silver atoms, not the spin of electrons. But as the atoms end up in a superposition of $| \uparrow, \text{path}_1 \rangle$ and $| \downarrow, \text{path}_2 \rangle$, measuring the position corresponds to measuring the spin at the same time.