1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Q:Is it possible to do a coordinate transfomation in momentum space?

  1. Sep 9, 2014 #1
    Q: How does one do a coordinate transformation in momentum space while insuring conservation of momentum?

    I have a several particles with momentum components [itex] P_x , P_y , P_z [/itex].
    I would like to rotate the x, y, and z axis. By angle θ in the x/y and angle Θ in the y/z .
    So giving new momentum [itex] P_x' , P_y' , P_z' [/itex].

    Is it possible to do this an conserve momentum while remaining in the lab frame? (The particles are relativistic but I don't believe this matters). What are the coordinate transformations?
     
  2. jcsd
  3. Sep 9, 2014 #2
    The conserved quantity is a vector, you can rotate the basis vectors however you want and it wouldn't change the magnitude of the vector.
     
  4. Sep 9, 2014 #3
    just to double check [itex] P^2=P_x^2 +P_y^2 +P_z^2=P_x'^2 +P_y'^2 +P_z'^2 [/itex] correct?
     
    Last edited by a moderator: Sep 9, 2014
  5. Sep 9, 2014 #4

    Nugatory

    User Avatar

    Staff: Mentor

    If you've done the transformation to the primed coordinates correctly, yes.

    In fact, HomogeneousCow has understated how much is conserved; the direction of the vector is also conserved. Of course it's a bit tricky talking about the "direction" of a vector when you don't have coordinate axes to make angles with - (1,0) in coordinates in which the x-axis points to the northeast is the same vector in the same direction as ##\sqrt{2}/2(1,1)## in coordinates in which the x-axis points east, but it's not obvious at all from the coordinates that that is so.

    However, the dot-product of two vectors is invariant under these coordinate transformations, and as the dot-product depends on the angle between the vectors, that gives us a coordinate-independent way of claiiming that direction is also invariant.
     
    Last edited: Sep 9, 2014
  6. Sep 9, 2014 #5
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Q:Is it possible to do a coordinate transfomation in momentum space?
  1. Q about momentum (Replies: 1)

Loading...