Multiphoton transitions for the harmonic oscillator

2- and 3-photon electric dipole transitions for the harmonic oscillator are shown to have zero intensity. This is extended to the general cases of Δv = n and Δv = n − 2 for n-photon transitions. Although not proved in general, it seems likely that all multiphoton transition moments vanish. This suggests that electric dipole multiphoton transition intensity is due to anharmonicity.