One-photon selection rules

In spectroscopy the quantum amplitude of a process is given by a matrix element of the form 〈 ψ _o | p | ψ _f 〉, where ψ _original is the wave function for the starting state of the transition, ψ _final is the final state, and p is the operator for a particular process, such as electric dipole moment, magnetic dipole moment, electric quadrupole moment, etc. In absorption spectroscopy, ψ _o is nearly always the ground state, and ψ _f is the excited state created by the absorption. In emission spectroscopy, vice-versa. It is frequently found that this matrix element vanishes, in which case the imagined process does not occur, and is called “forbidden”. What is not forbidden is “allowed”, and group theory makes it very easy to tell which is which for any given transition in any kind of spectroscopy (for any given spectroscopic operator p).