Photons electromagnetic field

Not only can electronic wavefiinctions tell us about the average values of all the physical properties for any particular state (i.e. above), but they also allow us to tell us how a specific perturbation (e.g. an electric field in the Stark effect, a magnetic field in the Zeeman effect and light s electromagnetic fields in spectroscopy) can alter the specific state of interest. For example, the perturbation arising from the electric field of a photon interacting with the electrons in a molecule is given within die so-called electric dipole approximation [12] by ... 

The acronym LASER (Light Amplification via tire Stimulated Emission of Radiation) defines the process of amplification. For all intents and purjDoses tliis metliod was elegantly outlined by Einstein in 1917 [H] wherein he derived a treatment of the dynamic equilibrium of a material in a electromagnetic field absorbing and emitting photons. Key here is tire insight tliat, in addition to absorjDtion and spontaneous emission processes, in an excited system one can stimulate tire emission of a photon by interaction witli tire electromagnetic field. It is tliis stimulated emission process which lays tire conceptual foundation of tire laser. 

In die presence of an electromagnetic field of energy of about our systems can undergo absorjDtive transitions from to E2, extracting a photon from die electric field. In addition, as described by Einstein, die field can induce emission of photons from 2 lo E (given E2 is occupied). Let die energy density of die external field be E(v) dren. 

As already mentioned, the results in Section HI are based on dispersions relations in the complex time domain. A complex time is not a new concept. It features in wave optics [28] for complex analytic signals (which is an electromagnetic field with only positive frequencies) and in nondemolition measurements performed on photons [41]. For transitions between adiabatic states (which is also discussed in this chapter), it was previously intioduced in several works [42-45]. 

Quantization of the Electromagnetic Field.—Instead of proceeding as in the previous discussion of spin 0 and spin particles, we shall here adopt essentially the opposite point of view. Namely, instead of formulating the quantum theory of a system of many photons in terms of operators and showing the equivalence of this formalism to the imposition of quantum rules on classical electrodynamics, we shall take as our point of departure certain commutation rules which we assume the field operators to satisfy. We shall then show that a... 

The expression for the rate R (sec ) of photon absorption due to coupling V beriveen a molecule s electronic and nuclear charges and an electromagnetic field is given through first order in perturbation theory by the well known Wentzel Fermi golden rule formula (7,8) ... 

A fourth possibility is electrodynamic bonding. This arises because atoms and molecules are not static, but are dynamically polarizable into dipoles. Each dipole oscillates, sending out an electromagnetic field which interacts with other nearby dipoles causing them to oscillate. As the dipoles exchange electro-magnetic energy (photons), they attract one another (London, 1937). 

Electric and magnetic effects have been observed since ancient times without suspecting a close relationship between the two phenomena, and certainly not inferring any close connection with visible light. The modern view is that the three effects are different aspects of a single concept, known as the electromagnetic field, which in turn is a manifestation of interactions involving the elementary entities called electrons and photons. 

Thus, if the normalization condition is satisfied, the energy of the electromagnetic field becomes identical with the photon energy. 

To express the angular momentum M of the electromagnetic field corresponding to one photon in terms of the wave function for the photon, M is identified with the expectation value of the angular momentum in the state... 

Note that dra(t)/dt = [H,ra]=(l/ma)[pa-qaA(ra)] and, consequently, the first term in (69) represents the kinetic energy of the system of particles in the presence of the transverse electromagnetic field. Note the analogy between this representation and the dynamical solute-solvent coupling of section 2.6 where the optical phonons are equivalent to electromagnetic photons of low frequency (the acoustical phonons are related to sound waves). 

We are now able to understand the response of our solid to an electromagnetic field oscillating at frequency >. For the sake of simplicity, we return to the use of expressions (4.17) and (4.18), related to a solid made of single-electron classical atoms, and to only one resonant frequency coq, related to the band gap. Using these expressions, in Figure 4.1(a) we have displayed the dependencies of si and si on the incident photon energy. 

The Time Dependent Processes Section uses time-dependent perturbation theory, combined with the classical electric and magnetic fields that arise due to the interaction of photons with the nuclei and electrons of a molecule, to derive expressions for the rates of transitions among atomic or molecular electronic, vibrational, and rotational states induced by photon absorption or emission. Sources of line broadening and time correlation function treatments of absorption lineshapes are briefly introduced. Finally, transitions induced by collisions rather than by electromagnetic fields are briefly treated to provide an introduction to the subject of theoretical chemical dynamics. 

For all of the cases considered earlier, a C(t) function is subjected to Fourier transformation to obtain a spectral lineshape function 1(G)), which then provides the essential ingredient for computing the net rate of photon absorption. In this Fourier transform process, the variable 0) is assumed to be the frequency of the electromagnetic field experienced by the molecules. The above considerations of Doppler shifting then leads one to realize that the correct functional form to use in converting C(t) to 1(G)) is ... 

In the previous section we presented the semi-classical electron-electron interaction we treated the electrons quantum mechanically but assumed that they interact via classical electromagnetic fields. The Breit retardation is only an approximate treatment of retardation and we shall now consider a more consistent treatment of the electron-electron interaction operator that also provides a bridge to relativistic DFT, which is current-density functional theory. For the correct description we have to take the quantization of electromagnetic fields into account (however, we will discuss only old, i.e., pre-1940 quantum electrodynamics). This means the two moving electrons interact via exchanged virtual photons with a specific angular frequency u>... 

The present chapter is devoted mainly to one of these new theories, in particular to its possible applications to photon physics and optics. This theory is based on the hypothesis of a nonzero divergence of the electric field in vacuo, in combination with the condition of Lorentz invariance. The nonzero electric field divergence, with an associated space-charge current density, introduces an extra degree of freedom that leads to new possible states of the electromagnetic field. This concept originated from some ideas by the author in the late 1960s, the first of which was published in a series of separate papers [10,12], and later in more complete forms and in reviews [13-20]. 

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