1. The problem statement, all variables and given/known data Prove that if two linear operators A and B commute and have non-degenerate eigenvalues then the two operators have common eigenfunctions. 2. Relevant equations [tex][A,B]= AB - BA= 0[/tex] [tex] Af=af[/tex] [tex] Bg=cg,\ let\ g=(f+1) --> B(f+1)=c(f+1)\ where\ a\neq c[/tex] 3. The attempt at a solution [tex]Af[B(f+1)]-B(f+1)[Af]=0[/tex] [tex]Af(Bf+B)-(Bf+B)Af=0[/tex] I have stopped here because I feel that I am on the wrong track. I have not used the fact that the eigenvalues are non-degenerate in this proof. Although continuation of what I am doing should show that the two operators commute..