(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Momentum operator eigenfunction problem

Can you offer guidance or do you also need help?

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