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: -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.