Transition dipole moment

Three wavefunction solutions to the time-dependent Schrödinger equation for an electron in a harmonic oscillator potential. Left: The real part (blue) and imaginary part (red) of the wavefunction. Right: The probability of finding the particle at a certain position. The top row is an energy eigenstate with low energy, the middle row is an energy eigenstate with higher energy, and the bottom is a quantum superposition mixing those two states. The bottom-right shows that the electron is moving back and forth in the superposition state. This motion causes an oscillating electric dipole moment, which in turn is proportional to the transition dipole moment between the two eigenstates.

The transition dipole moment or transition moment, usually denoted $\mathbf {d} _{nm}$ for a transition between an initial state, $m$ , and a final state, $n$ , is the electric dipole moment associated with the transition between the two states. In general the transition dipole moment is a complex vector quantity that includes the phase factors associated with the two states. Its direction gives the polarization of the transition, which determines how the system will interact with an electromagnetic wave of a given polarization, while the square of the magnitude gives the strength of the interaction due to the distribution of charge within the system. The SI unit of the transition dipole moment is the Coulomb-meter (Cm); a more conveniently sized unit is the Debye (D).