Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Probability of simultaneous measurements of momentum and position

  1. Mar 1, 2009 #1
    Given a three- dimensional wavefunction (phi) (x, y, z),
    what is the probability of simultaneously measuring
    momentum and position to obtain the results
    a < y < b and p' < Pz < P" ?
    I know that integration of the square norm of the wavefunction of the region
    under question yields the probability for finding the position or momentum
    of the system described by the wavefunction. But how do you do this
    for simultaneous measurements of momentum and position?

  2. jcsd
  3. Mar 1, 2009 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    What do you mean by "simultaneous measurement"? One single measurement that immediately produces both values of the observable? Don't you think that if this is the case, then it doesn't matter how we proceed with the sequence of AB versus BA for non-commuting observables?

  4. Mar 1, 2009 #3
    x, y, and pz are three mutually commuting observables, so it would be convenient to write your wave function in the corresponding basis (phi)(x, y, pz). (To do that, you can perform a Fourier transform of your position-space wave function (phi) (x, y, z) on the variable z.) The next step would be to take the square of the modulus |(phi)(x, y, pz)|^2 and integrate it on the given region of y and pz.
  5. Mar 2, 2009 #4
    Sorry to ZapperZ for ambguities in phrasing. However, meopemuk's answer was the one I was looking for. Thanks!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Probability of simultaneous measurements of momentum and position
  1. Position Measurement (Replies: 1)