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Homework Help: 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
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