Main Question or Discussion Point
How do we measure a quantum particle's momentum?
There are no unique methods to do this. In http://arxiv.org/abs/cond-mat/0209476" [Broken] (ARPES), the detector has a finite rectangular slit in which one dimension is the energy, while the other is the momentum of the emitted photoelectrons. So you would get a raw image of something like my avatar. For certain types of material (such as 2D, layered material), the transverse momentum of the photoelectrons corresponds to the transverse momentum of such electrons while it is in the material.How do we measure a quantum particle's momentum?
Measurement of momentum is always achieved by measurement of position, so I assume that observation of momentum is not how it IS but how it WAS . After measurement of momentum value p, the state cannot keep on |p>. It is a kind of destructive observation.So do all the methods amount to making a position measurement from which we infer the momentum? How does that square with the uncertainty principle?
This is a very important point that IMO is *way* under-emphasized in discussions of QM. We talk rather blithely about measurement of observables in an experimental sense, however the reality is that every measurement we can actually *do* involves either an explicit or implicit measurement of position to one extent or another. The closest thing to a counter-example that I can think of right away might be a direct absorption spectroscopy experiment on a gas confined to a large-volume sample cell. In that case the "uncertainty" in the position of the gas molecules giving rise to the observed spectral lines is fairly large, however you can still say with certainty that they must have been somewhere inside the cell at the time they absorbed a photon(s). So even there there is an implicit measurement of position involved.Hi.
Measurement of momentum is always achieved by measurement of position, so I assume that observation of momentum is not how it IS but how it WAS . After measurement of momentum value p, the state cannot keep on |p>. It is a kind of destructive observation.