If a hamiltonian remains unchanged by an operation like translation or rotation, then the corresponding operator commutes with the hamiltonian. Some examples of this are the free particle hamiltonian p²/2m and translation, the harmonic oscillator hamiltonian and inversion (x <--> -x), and a central potential and rotation. If an operator commutes with the hamiltonian, then one can find simultaneous eigenvalues of the hamiltonian and the operator. For a continuous symmetry like translation or rotation, one can build up any translation or rotation from infinitesimal ones. A finite tranlation or rotation may be written as T(a) = exp(-i(a/hbar)p) and R(theta) = exp(-i(theta/hbar)L_n), respectively, where p is the momentum operator and L_n is the angular momentum operator along the axis of rotation. The fact that rotations in three dimensions do no commute then implies the commutation relations of the angular momentum operators. An interesting application of this formula for the rotations is that rotating a spin 1/2 particle by 360 degrees gives a phase factor of -1.