Operator electric field

If we decompose the electric field operator into a transverse and longitudinal part... 

But why determine the free energies of adsorption from experiment Instead, one can attempt to calculate the values from a knowledge of the particles, the forces between them, and the effect on the particles of the electric field operating on the electrified interface. 

The driving force for ionic drift, i.e., the electric field X, not only has a particular magnitude, it also acts in a particular direction. It is a vector. Since the ionic current density j, i.e., the flow of electric charge, is proportional to the electric field operating in a solution [Eq. (4.128)],... 

The relation between the positive frequency part of the electric field operator at a point R RR in the far-field zone of the radiating systems and the dipole moments is given by the well-known expression [4,20]... 

The equations of motion (96) can be used to calculate the steady-state fluorescence spectrum of the driven atom. The spectrum is defined as the Fourier transform of the stationary value of the two-time correlation function of the electric field operators... 

The atoms interact with the quantized three-dimensional vacuum field and are also driven by a single-mode coherent laser field. We express the quantized multimode field in terms of the annihilation and creation operators and a x of field mode kr, which has wavevector k, frequency cd., and polarization ets. Thus, we write the electric field operator at position r in the form... 

The positive-frequency part of the electric field operator 1 has the form... 

Significantly, the results of Eqs. (62) and (63) closely resemble those calculated using the more familiar vacuum electric field operators, modified by the... 

Using the electric field operator E (see eqn 4.47) in the Heisenberg representation, we obtain... 

Eq. (8). The value of P is, however, slightly greater than the predictions of these models. This difference is presumably caused by nonlocal effects produced by the electric field operating at the growing interfiice [20]. Likewise, the difference in the value of yff leads to z 3, and a coarsening exponent 1/z 0.33. 

Thereby, d is the material dipole operator. The positive frequency component of the electric field operator is denoted by... 

Since the two-level system is located in a half-open space we start by expanding the electric field operator (10) in mode functions suitable for the parabolic symmetry of the problem. Following the results of Ref. [47] we use mode functions of the form... 

Interaction with the vacuum (Fig. 3.5a). In contemporary physics theory, the perfect vacuum does not just represent nothing. The electric field of the vacuum itself fluctuates about zero and these instantaneous fluctuations influence the motion of any chaiged particle. When a strong electric field operates in a vacuum, the latter undeigoes a polarization (called vacuum polarizfition), which means a spontaneous creation of matter, and more specifically, of particle-antiparticle pairs. 

As a result of the complexity of this dielectric force phenomenon, many spatially nonuniform geometries and electric field operating conditions are possible. Specifically in DC fields, the nonuniform insulator geometry of obstacles results in a dielectrophoretic force acting on the polarized particle, which causes the particle to move either toward or away firom electric field intensity without having the cells in direct contact with the electrode. 

Here, q is the density operator for the field, and E and E represent the negative- and positive-frequency portions of the electric field operator , respectively. We assume that the final state of the detector is much broader than the bandwidth of the incident radiation, and that a broad band of final states is accessible [7.36, 37]. 

If we specifically consider the mixing of two single-mode, amplitude-stabilized, first-order coherent waves, both of which are well collimated, parallel, plane polarized along a common unit vector, and normally incident onto a photosensitive material, we may write the positive portion of the electric field operator as the superposition of two scalar fields... 

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