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!

Momentum operator eigenfunction problem

  1. Feb 6, 2012 #1
    1. The problem statement, all variables and given/known data

    Given f(x)1 = cos(kx) and f(x)2 = sin(kx), find a linear combination which is an eigenfunction of the momentum operator.



    2. Relevant equations

    The momentum operator: 03fb1cbecde94fce084d8ecd087b7d43.png


    -iħ d\dx(Acos(kx)+Bsin(kx) = λ[Acos(kx) + Bsin(kx)] where λ is some constant.

    3. The attempt at a solution

    I've tried a few different A's and B's, mainly permutations of -1 and 1, but I honestly can't see how this is doable. No matter what you do the derivatives' signs aren't going to behave the same way so I just don't see how you can get the same function back out after taking the derivative, no matter what constants you multiply them by.


    Edit: Nevermind, figured it out.

    Edit 2: Occurs to me that just in case someone is looking for this question on google or something in the future, I should post the solution I got. Answer was A = 1 B = i.
     
    Last edited: Feb 6, 2012
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted