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To let you know where I stand, I am aware of the formal quantum theory (Hilbert space formulation).

As you know, it states that an observable is an operator, and that's fine.

My question is the following: what is the concrete realization of a measuring apparatus? The theory says "physically we're looking at the concept of position, this means you have to use this certain operator" and it is silent about the construction of the measurement apparatus. Can somebody tell me about a (relatively simple) position measuring apparatus? If possible, also for measuring impulse?

One often hears about the following primitive position measurement apparatus (which, I presume, one has to describe on a classical level, otherwise one gets into an endless generalization of the wavy quantum system):

one fires of a photon from a certain position, it bumps into the electron (which I take as my system) and bounces back to a certain final position

Now, how exactly does this give you information about position? If I understand correctly, the apparatus now has three numbers: the place the photon was fired from, the time it was underway, and the place where the photon came back. How do we combine these numbers to give a rough estimate of position (if even only conceptually)? Or is this a bad example of a position measurement? What is it lacking?

Furthermore, am I allowed to say that the wave function of the electron has thus collapsed? (I understand the ontological status of the psi is still up for discussion, but all I'm interested in at the moment is in knowing if I can talk about the collapse [in this situation] in a consistent way) So shortly after this photon-electron interaction, the psi (more exactly: its resulting probability distribution) is a delta function? This would mean that at that same moment, nothing is known about velocity (property of Fourier analysis).

I often hear as a physical argument for that latter: ah yes, the photon has interacted with the particle and has given it some impulse and energy.

Is this latter way of thinking consistent? Is it made up? How can any speed be possible, given that the photon had only a finite energy to begin with? Surely the system (= electron) cannot have gained more energy than the photon had to begin with.

I welcome all replies,

thank you.