Quantum Theory of Molecules in Static Electric Fields

2 QUANTUM THEORY OF MOLECULES IN STATIC ELECTRIC FIELDS 

We will be concerned almost exclusively with interactions between light and isolated molecules. The total Hamiltonian of the system is then given by 

The unperturbed molecular states P depend on both position (r) and time (t) since they are eigenstates of /Iq, they can be factorized into spatial and time-dependent portions, 

instead of (1.12), the total Hamiltonian for the molecule in the presence of light were H = Hq + the eigenstates of the system would become simple products of molecular and radiation field states T (r, t) IXrad) where the radiation field states Xrad would depend on photon occupation numbers, energies and polarizations. Since no coupling of light with molecular states is implied in such a Hamiltonian, no transitions can occur between molecular states due to absorption or emission of light in this description. The simplest Hamiltonian that can account for spectroscopic transitions is therefore the one in Eq. 1.12. 

For molecules subjected to static (time-independent) electromagnetic fields, the perturbed energies and eigenstates may be evaluated from stationary-state perturbation theory [3]. The full Hamiltonian may be written in terms of a perturbation parameter A (which may be set to unity at the end of the calculation, after serving its usual purpose of keeping track of orders in the perturbation expansions for the energies and eigenstates) as 

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