Hello, so I have a couple of related questions. 1) If you have a wavefuction Ψ, and act on it with some operator, does it have to give you the same wavefunction back (ie. does the wavefunction have to be an eigenfunction of the operator)? Could you have a wavefunction like e-iħtSin(x)? Since this is an eigenfunction of the energy operator but not the momentum operator. I ask this because if Ψ is an eigenfunction of the momentum operator then it would have a definite momentum given by the eigevalue. I believe this is correct anyway. So if Ψ is not an eigenfunction of the operator you would not have a definite value for measuring that observable, then would you return some uncertainty in the observed value? 2) If you have Ψ= ekx, then is Ψ not an eigenfunction of both the position and momentum operators? I'm struggling with this one since that would mean it has both a definite position and momentum, but since these operators are non-commutative there should be some uncertainty and so surely you can't have a definite answer for both?