Transition dipole moment

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The Transition dipole moment or just Transition moment, is a term usually denoted $μ n m$ .

An oscillating electric or magnetic moment can be induced in an atom or molecule by an electromagnetic wave. Its interaction with the electromagnetic field is resonant if the frequency of the latter corresponds to the energy difference between the initial and final states of a transition ( $E = h ν$ ). The amplitude of this moment is referred to as the transition dipole moment. It 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 dipole moment operator $\vec{d}$

$\vec{d} = e(\sum_i x_i, \sum_i y_i, \sum_i z_i)$

where the summations are over the coordinates of the elementary charges.

$\mu_{nm} = \int \Psi^*_n \,\, \vec{d} \,\, \Psi_m \, d^3r = \langle\Psi_n|\,\vec{d}\,|\Psi_m\rangle$

Its sign is arbitrary, its direction defines the direction of transition polarization, and its square determines the strength of the transition. If e is omitted one obtains $R n m$ in the sense used in oscillator strength. The SI unit of the transition dipole moment is C m. The common unit is the Debye (D).