text: For a transition where a single charged particle changes state from  to , the transition dipole moment  is
  where q is the particles charge, r is its position, and the integral is over all space ( is shorthand for ). The transition dipole moment is a vector; for example its x'-component is
  In other words, the transition dipole moment can be viewed as an off-diagonal matrix element of the position operator, multiplied by the particle's charge.