Electrical oscillator

The oscillating electric dipole density, P (the polarization), that is induced by the total incident electric field,... 

The interaction of electromagnetic radiation with matter can be explained using either the electric field or the magnetic field. For this reason, only the electric field component is shown in Figure 10.2. The oscillating electric field is described by a sine wave of the form... 

Thus, for X = y, F = 0 which gives rise to planes of zero field strength (Figure 25.2b). At all other positions between the poles, the oscillating electric field (F) causes ions to be alternately attracted to and repelled by the pairs of rods (A, B Figure 25.2). 

In this discussion we define the x direction to be the direction of propagation of the light waves. This means that the yz plane contains the oscillating electrical and magnetic fields which carry the energy of the radiation. Only the electric field concerns us in scattering. Since the oscillation is periodic in both time t and location x, the electric field can be represented by the equation... 

As our discussion of scattering proceeds, we shall examine the coupling between the oscillating electrical field of light and the electrons of the scatterer in detail. First, it is useful to consider the interaction of an electric field with matter, as this manifests itself in the dielectric behavior of a substance. This will not only introduce us to the field-matter interaction, but will also provide some relationships which will be useful later. 

When monochromatic radiation falls on a molecular sample in the gas phase, and is not absorbed by it, the oscillating electric field E (see Equation 2.1) of the radiation induces in the molecule an electric dipole which is related to E by the polarizability... 

These are polarized along the z, x andy axes, respectively, since they involve and This means that when, for example, a — Aj transition occurs an oscillating electric dipole is set up along the x axis. 

In the context of discussion of the Raman effect, Equation (5.43) relates the oscillating electric field E of the incident radiation, the induced electric dipole fi and the polarizability a by... 

Answer. The third term in equation (9.11) involves the cube of the oscillating electric field which (cf. Equation 9.13) is given by... 

All these results generalize to homogeneous linear differential equations with constant coefficients of order higher than 2. These equations (especially of order 2) have been much used because of the ease of solution. Oscillations, electric circuits, diffusion processes, and heat-flow problems are a few examples for which such equations are useful. 

We have seen above how to calculate polarizabilities and hyperpolarizabilities for statie electric fields. I will consider a simple oscillating electric field... 

Maxwell in 1873 who postulated that an oscillating electrical circuit should radiate electromagnetic waves... 

We only consider static response properties in this chapter, which arise from fixed external field. Their dynamic counterparts describe the response to an oscillating electric field of electromagnetic radiation and are of great importance in the context of non-linear optics. As an entry point to the treatment of frequency-dependent electric response properties in the domain of time-dependent DFT we recommend the studies by van Gisbergen, Snijders, and Baerends, 1998a and 1998b. 

The oscillating electric and magnetic fields of a beam of ordinary light in one plane. The waves depicted here occur in all possible planes in ordinary light. 

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