# How is Momentum Measured?

Nicky
What kind of experimental apparatus provides the purest measurement of a low-energy particle's momentum? By "pure" momentum measurement, I mean allowing for the maximum achievable uncertainty in position, and therefore the most accurate possible reading of momentum as per the uncertainty principle.

## Answers and Replies

Homework Helper
Gold Member
Momentum is usually measured by R=pc/qB (in Gaussian units).
The measurement is of the radius of the path of a moving particle of charge q i a magnetic field B..

Nicky
Meir Achuz said:
Momentum is usually measured by R=pc/qB (in Gaussian units).
The measurement is of the radius of the path of a moving particle of charge q i a magnetic field B..

I am trying to imagine how one would display interference effects analogous to the double-slit experiment, except that the roles of position and momentum are reversed. With the usual double-slit setup, the beam components passing through the two slits interfere, resulting in some spots on the detection screen that receive less total particle flux. So in the alternative experiment, I guess interference would be manifest as certain path radii showing stronger particle flux than others.

How to produce the two interfering beams is less clear. Maybe a single beam could be split into two, somehow doppler shift one of the two beams, then recombine the two beams to form a superposition of momentum states. Has anything like this been attempted?

Staff Emeritus
Gold Member
Nicky said:
What kind of experimental apparatus provides the purest measurement of a low-energy particle's momentum? By "pure" momentum measurement, I mean allowing for the maximum achievable uncertainty in position, and therefore the most accurate possible reading of momentum as per the uncertainty principle.

Xtal diffraction ! At least, that's how it is done with slow neutrons: a monochromator is nothing else but a pure monocrystal (for instance, of silicium) and by selecting an outgoing angle you impose a Bragg condition and hence a pure momentum.
The bigger and the purer the Xtal is, the better your momentum selection (and of course the worse your position, because it is limited to the entire Xtal).

cheers,
Patrick.

Staff Emeritus
Nicky said:
What kind of experimental apparatus provides the purest measurement of a low-energy particle's momentum? By "pure" momentum measurement, I mean allowing for the maximum achievable uncertainty in position, and therefore the most accurate possible reading of momentum as per the uncertainty principle.

How about a hemispherical electron analyzer?

My avatar is actually a 2D plot of E vs. k of electrons coming out of a material from a photoemission process and into a Scienta SES200 electron analyzer. And we all know that "k" is equivalent to the momentum, in this case, the momentum of the electron and the crystal. ("crystal momentum") So the horizontal axis is really the momentum of the electrons. And these ARE low energy electrons, with energy in the range of ~0 to about 10 eV.

This is now a common technique in angle-resolved photoemission spectroscopy (ARPES), so most papers using this technique will have references to it.

Zz.