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For a transition where a single charged particle changes state from to , the transition dipole moment is

where q is the particle's 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.

Multiple charged particles

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