Position vs momentum measurement

[hokhani]

TL;DR

Does measurement of momentum like position requires a detector to cover all the momentums?

To measure the position of a quantum particle it seems that the detector must covers all the positions to detect the particle at one point. How about the measurement of momentum? Does this measurement require the momentum detector to cover all the possible values of momentum to show one of the momentum eigenvalues?

 

[Demystifier]

Yes.

 

[Andy Resnick]

TL;DR: Does measurement of momentum like position requires a detector to cover all the momentums?

To measure the position of a quantum particle it seems that the detector must covers all the positions to detect the particle at one point. How about the measurement of momentum? Does this measurement require the momentum detector to cover all the possible values of momentum to show one of the momentum eigenvalues?

I guess it depends on what information you hope to obtain- a point detector does not cover all positions, but then your location measurement is simply 'yes' or 'no' (of course, since you set the position of the detector, you also know the position value). Similarly, a momentum measurement can be likewise performed- a magnet and slit is a momentum filter/selector for charged particles- but your measurement is simply 'yes' or 'no'.