Quantum optics generalized model

The most simple, but general, model to describe the interaction of optical radiation with solids is a classical model, due to Lorentz, in which it is assumed that the valence electrons are bound to specific atoms in the solid by harmonic forces. These harmonic forces are the Coulomb forces that tend to restore the valence electrons into specific orbits around the atomic nuclei. Therefore, the solid is considered as a collection of atomic oscillators, each one with its characteristic natural frequency. We presume that if we excite one of these atomic oscillators with its natural frequency (the resonance frequency), a resonant process will be produced. From the quantum viewpoint, these frequencies correspond to those needed to produce valence band to conduction band transitions. In the first approach we consider only a unique resonant frequency, >o in other words, the solid consists of a collection of equivalent atomic oscillators. In this approach, coq would correspond to the gap frequency. 

The branch of quantum optics studying the processes of interaction of one or a few atoms with the quantized cavity modes is usually called cavity quantum electrodynamics (cavity QED). The theoretical concepts of cavity QED are based in the first place on investigation of the Jaynes-Cummings model [67] and its generalizations (for a review, see Ref. 68). The reason for this is that the model describes fairly well the physical processes under consideration and at the same time admits an exact solution. 

The combination of the cluster model approach and modem powerful quantum chemistry techniques can provide useful information about the electronic structure of local phenomena in metal oxides. The theoretical description of the electronic states involved in local optical transitions and magnetic phenomena, for example, in these oxides needs very accurate computational schemes, because of the generally very large differential electron correlation effects. Recently, two very promising methods have become available, that allow to study optical and magnetic phenomena with a high degree of precision. The first one, the Differ-... 

The next section (Sect. 2) is devoted to a lengthy discussion of the molecular hypothesis from the point of view of quantum field theory, and this provides the basis for the subsequent discussion of optical activity. Having used linear response theory to establish the equations for optical activity (Sect. 3), we pause to discuss the properties of the wavefunctions of optically active isomers in relation to the space inversion operator (Sect. 4), before indicating how the general optical activity equations can be related to the usual Rosenfeld equation for the optical rotation in a chiral molecule. Finally (Sect. 5), there are critical remarks about what can currently be said in the microscopic quantum-mechanical theory of optical activity based on some approximate models of the field theory. 

These equations are used in semiempirical quantum chemical calculations of non-linear optical polarizabilities by applying perturbation theoretical expressions [the so-called sum-over-states (SOS) method]. Here we use them to derive some qualitative and very general trends in a few simple model systems. To this end we concentrate on the electronic structure, i.e. on the LCAO coefficients. We do not explicitly calculate the transition frequencies. This is justified for the qualitative discussion below since typical transition energies... 

The luminescence of small particles, especially of semiconductors, is a fascinating development in the field of physical chemistry, although it is too early to evaluate the potential of these particles for applications. The essential point is that the physical properties of small semiconductor particles are different from the bulk properties and from the molecular properties. It is generally observed that the optical absorption edge shifts to the blue if the semiconductor particle size decreases. This is ascribed to the quantum size effect. This is most easily understood from the electron-in-a-box model. Due to their spatial confinement the kinetic energy of the electrons increases. This results in a larger band gap (84). 

In the Raman case, three distinct general computational thedries have been proposed the bond polarizability theory, the atom dipole interaction theory and localized molecular orbital theories. In the first and third of these the normal modes of vibration, and hence the vibrational quantum states, must embrace a chiral nuclear framework. They are therefore analogous to the inherently chiral chromo-phore model of electronic optical activity in which the electronic states are delo-... 

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