1. The problem statement, all variables and given/known data A measurement is described by the operator: |0⟩⟨1| + |1⟩⟨0| where, |0⟩ and |1⟩ represent orthonormal states. What are the possible measurement outcomes? 2. Relevant equations Eigenvalue Equation: A|Ψ> = a|Ψ> 3. The attempt at a solution Apologies for the basic question but just very unsure of myself when it comes to this stuff. I have had a go and come up with a solution but I'm not sure if its right so any help would be much appreciated. We're told that: A = |0⟩⟨1| + |1⟩⟨0| Can I then assume something like: Ψ = α|1> + β|0>? using this I've then solved the eigenvalue equation, AΨ=aΨ, and found: α|0> + β|1> = aα|1> + aβ|0> giving: α=aβ & β = aα thus, β=a2β a = (+-) 1 hence, my eigenvalues are -1 and 1. and these are the possible outcomes?