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Is it possible to build an apparatus that could do the following (at least ideally in principle)? If so, what would it be like?

A fairly localized light wave packet (with a corresponding spread in momentum) reaches the origin of our coordinate system from any direction in the XY plane (taking 2 dimensional case for simplicity).

It now interacts with the apparatus.

After the interaction, a pointer points along a certain direction which is the direction of the measured momentum. Another analog pointer with a scale shows the magnitude of the momentum. (Or maybe two pointers for the X and Y momentum respectively).

Meanwhile, the wave packet is instantly (?) converted into a highly extended, nearly plane wave -- ideally extending over all of space, since it has to be a momentum eigenstate. Of course, the pointer readings have to be consistent with the wave number of this extended wave.

A fairly localized light wave packet (with a corresponding spread in momentum) reaches the origin of our coordinate system from any direction in the XY plane (taking 2 dimensional case for simplicity).

It now interacts with the apparatus.

After the interaction, a pointer points along a certain direction which is the direction of the measured momentum. Another analog pointer with a scale shows the magnitude of the momentum. (Or maybe two pointers for the X and Y momentum respectively).

Meanwhile, the wave packet is instantly (?) converted into a highly extended, nearly plane wave -- ideally extending over all of space, since it has to be a momentum eigenstate. Of course, the pointer readings have to be consistent with the wave number of this extended wave.

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