Electric dipole transitions time-dependent perturbation theory

In quantum mechanics the definition of molecular polarizabilities is given through time-dependent perturbation theory in the electric dipole approximation. These expressions are usually given in terms of sums of transition matrix elements over energy denominators involving the full electronic structure of the molecule [42]. 

Time-dependent perturbation theory is applied to study electric dipole transitions. We give a brief introduction and quote some of the results. The Hamiltonian... 

As mentioned, the most attractive properties of these systems used in their applications originate from the electric dipole/ <—> / transitions. They might be direct and observed as absorption or emission, or play a role as initial and final steps of sensitized luminescence, for example. In all of these cases the amplitude of the electric dipole transition is determined by the certain order of the time-dependent perturbation theory applied for the description of the interaction between matter and the radiation field. Each order of the perturbing expansion... 

According to Fermi s golden rule [40, 42], the integral intensity A of the absorption band of the normal mode is proportional to the probability per unit time of a transition between an initial state i and a final state j. Within the framework of the first (dipole) approximation of time-dependent perturbation quantum theory [46, 65], this probability is proportional to the square of the matrix element of the Hamiltonian H = —E p, where E is the electric field vector and p is the electric dipole moment, resulting in the absorption... 

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