I have a question regarding an exercise I am doing. It is an electron confined to move on a cylinder and I am asked to: "Find the expectation value of Ly and Lz" in the unperturbed basis. I am just not sure what is meant by the expectation value in a basis? I know what the expectation value is if you give me some wave function at time t. Then <operator> is just: <operator> = <ψloperatorlψ> But what on earth is an "expectation value in a basis"? It is probably something pretty straightforward like the expectation value for the nth eigenfunction, but I just want to be sure.