Wave equation photon

Spin 1, Mass Zero Particles. Photons.—For a mass zero, spin 1 particle, the set of relativistic wave equations describing the particle is Maxwell s equations. We adopt the vector 9(x) and the pseudovector (x) which are positive energy (frequency) solutions of... 

We shall adopt Eqs. (9-510) and (9-511) as the covariant wave equation for the covariant four-vector amplitude 9ttf(a ) describing a photon. The physically realizable amplitudes correspond to positive frequency solutions of Eq. (9-510), which in addition satisfy the subsidiary condition (9-511). In other words the admissible wave functions satisfy... 

The time-dependence of the photon wave equation in momentum space... 

Bhabha treated the general relativistic wave equations and Tonnelat presented the idea of Louis de Broglie of trying to describe a photon as an object composed of two neutrinos.63... 

In this section we discuss the nonrelativistic 0(3) b quantum electrodynamics. This discussion covers the basic physics of f/(l) electrodynamics and leads into a discussion of nonrelativistic 0(3)h quantum electrodynamics. This discussion will introduce the quantum picture of the interaction between a fermion and the electromagnetic field with the magnetic field. Here it is demonstrated that the existence of the field implies photon-photon interactions. In nonrelativistic quantum electrodynamics this leads to nonlinear wave equations. Some presentation is given on relativistic quantum electrodynamics and the occurrence of Feynman diagrams that emerge from the B are demonstrated to lead to new subtle corrections. Numerical results with the interaction of a fermion, identical in form to a 2-state atom, with photons in a cavity are discussed. This concludes with a demonstration of the Lamb shift and renormalizability. 

Munera and Guzman [56] obtained new explicit noncyclic solutions for the three-dimensional time-dependent wave equation in spherical coordinates. Their solutions constitute a new solution for the classical Maxwell equations. It is shown that the class of Lorenz-invariant inductive phenomena may have longitudinal fields as solution. But here, these solutions correspond to massless particles. Hence, in this framework a photon with zero rest mass may be compatible with a longitudinal field in contrast to that Lehnert, Evans, and Roscoe frameworks. But the extra degrees of freedom associated with this kind of longitudinal solution without nonzero photon mass is not clear, at least at the present state of development of the theory. More efforts are needed to clarify this situation. 

As can be seen from the equations (21)-(22) and (23)-(24), there is an essential difference between the representations of plane and multipole waves of photons. In particular, a monochromatic plane wave of photons is specihed by only two different quantum numbers a = x, y, describing the linear polarization in Cartesian coordinates. In turn, the monochromatic multipole photons are described by much more quantum numbers. Even in the simplest case of the electric dipole radiation when X = E and j = 1, we have three different states of multipole photons in (23) with m = 0, 1. Besides that, the plane waves of photons have the same polarization a everywhere, while the states of multipole photons have given m. It is seen from (24) that, in this case, the polarization described by the spin index p can have different values at different distances from the singular point. In Section V we discuss the polarization properties of the multipole radiation in greater detail. 

Analysis of the photonic LDOS relies on electromagnetic wave equations derived from Maxwell s equations. Electromagnetic properties of the scatterer can be evaluated by solving the vector wave equations, where the boundary condition near the scatterer is appropriately taken into account. The vector wave equation at... 

In this subsection, we will investigate the propagation dynamics of an incident probe pulse in ultracold atoms aroimd a photonic bandgap induced by a time-independent SW coupling. Then it is necessary to resort to the Maxwell wave equations coupled with the density matrix equations, i.e. the cowpled Maxwell-Liouville equations. In particular, when the probe is very weak,... 

This means that for each incident photon of frequency 0)2 there are two outgoing photons of the same frequency. Simultaneously with the generation of a new wave of frequency co - the incident wave of frequency (O2 is parametrically amplified. If the nonlinear medium is placed between two mirrors reflecting at the frequencies (O2 and (or) ( 3, this parametric effect may be increased. One calls such a device a parametric oscillator (see Figure 3). From this point of view, co = (o corresponds to the so-called pump wave, (jl>2 = (o to the (amplified) signal wave, and (03 = (Oi- CO2) =o)i to the idler wave. Equation [8] may be simplified to... 

We consider here excitation by high intensity radiation with many photons (quanta) per quantum field mode which can for all practical purposes be described as a classical electromagnetic wave satisfying the general wave equations (2) and (3) ... 

As is the case with molecular quantities, Fourier components of E and P are accompanied by frequency-dependent, complex susceptibilities % The macroscopic susceptibilities are used in the physical description of NLO effects, such effects typically being analyzed using wave equations in which the nonlinear polarization produced by a given type of interaction constitutes a source term. Quantities other than the susceptibilities are often used for describing specific NLO interactions. The most useful of these are the electro-optic coefficient r related to co ca,0), the nonlinear refractive index ti2, related to the real component of the degenerate third-order susceptibility Re(x —m,ai)), and the two-photon absorption coefficient jSg, related to the corresponding imaginary component Im(x —[Pg.66]

Determination of the photon density requires knowledge of the number of modes that can be accommodated in a cavity [34]. To find this one should begin with the wave equation... 

The energies of the various contributions are quantised , i.e., in a given state the isolated molecule may possess one of a discrete set of values these values are often referred to as energy levels. When a molecule absorbs light, its energy is momentarily increased by an amount equal to that of the photon. The energy is related to the wave length (X) and frequency (v) by the equation ... 

In Equation (9.18) we have treated Vj and V2 differently by involving two photons of Vj and only one of V2. However, four-wave mixing involving one photon of Vj and two of V2 to produce V4, represented by... 

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