**Transition Dipole Moment** When a system interacts with an electromagnetic wave of frequency ν, it can undergo a transition from an initial to a final state of energy difference E=hν through the coupling of the electromagnetic field to the transition dipole moment.

If the charge e is omitted from the electric dipole operator during this calculation, one obtains as used in oscillator strength.

Another definition:

An oscillating electric or magnetic moment can be induced in an atom or molecule by an electromagnetic field. The interaction with the electromagnetic wave is resonant if the frequency of the field corresponds to the energy difference between the initial and final states of a transition (ΔE = hν). The amplitude of this moment is referred to as the transition moment.

The transition dipole moment can be calculated from an integral taken over the product of the wavefunctions of the initial (m) and final (n) states of a spectral transition and the appropriate dipole moment operator of the electromagnetic radiation:

d

_{nm} = <n|d|m> where operator d = e(∑

_{i}x

_{i}, ∑

_{i}y

_{i}, ∑

_{i}z

_{i})

The transition dipole moment is useful for determining if transitions are allowed under the electric dipole interaction.

__Source:__ http://en.wikipedia.org/wiki/Transition_dipole_moment