Selection Rules for Hydrogen Absorption

This is the first example we will encounter of selection rules for allowed transitions. Physically, the selection rules arise because the electric field needs a dipole moment in order to interact with the atom, and only these specific changes in the quantum numbers create a dipole moment. More generally, the selection rules for absorption in a hydrogen atom are 

There is nothing special about the choice of the z-axis for a hydrogen atom. If we had used x-polarized radiation, we would have excited npx states y-polarized radiation would have excited npy states. Either of these are combinations of // / = +1 and 

FIGURE 8.3 Allowed absorptions from the Is state for hydrogen (levels with n 4 omitted for clarity) which satisfy the selection rules presented in Equations 8.3 and 8.4. 

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