Answer to Question #72730 in Algebra for rudi

Question

hi , I have a Hamiltonian of NxN matrix when I diagonalize it I got N different eigenstates , I observe that there is an operator say "O" when acting on the eigenstates of the Hamiltonian gives 1 or -1 in strange order which I try hard to understand but I couldn't , is there any mathematical suggestion I could do to understand . thanks in advance