Electromagnetic quantization

The energy of an elastic wave in a solid is quantized just as the energy of an electromagnetic wave in a cavity. 

In the course of his research on electromagnetic waves Hertz discovered the photoelectric effect. He showed that for the metals he used as targets, incident radiation in the ultraviolet was required to release negative charges from the metal. Research by Philipp Lenard, Wilhelm Hallwachs, J. J. Thomson, and other physicists finally led Albert Einstein to his famous 1905 equation for the photoelectric effect, which includes the idea that electromagnetic energy is quantized in units of hv, where h is Planck s con-... 

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... 

It should be stressed, however, that the introduction of the operator 2(k) in the present context is purely for mathematical convenience. All the subsequent development could also be carried out without its introduction. It is only when we consider the interaction of the quantized electromagnetic field with charged particles that the potentials assume new importance—at least in the usual formulation with its particular way of fixing the phase factors in the operators of the charged fields—since the potentials themselves then appear in the equations of motion of the interacting electromagnetic and matter fields. 

Before embarking on the problem of the interaction of the negaton-positon field with the quantized electromagnetic field, we shall first consider the case of the negaton-positon field interacting with an external, classical (prescribed) electromagnetic field. We shall also outline in the present chapter those aspects of the theory of the S-matrix that will be required for the treatment of quantum electrodynamics. Section 10.4 presents a treatment of the Dirac equation in an external field. 

For a discussion of the quantized electromagnetic field interacting with a given (prescribed) external current, see ... 

We shall adopt these variables as the dynamical variables describing the quantized electromagnetic field. 

Dirac s density matrix, 422 Dirac s quantization of the electromagnetic field, 485... 

Eigenstates of a crystal, 725 Eigenvalues of quantum mechanical angular momentum, 396 Electrical filter response, 180 Electrical oscillatory circuit, 380 Electric charge operator, total, 542 Electrodynamics, quantum (see Quantum electrodynamics) Electromagnetic field, quantization of, 486, 560... 

Studies of black-body radiation led to Planck s hypothesis of the quantization of electromagnetic radiation. The photoelectric effect provides evidence of the particulate nature of electromagnetic radiation. 

Statistical properties of light are described within the framework of quantum optics which is based on a quantized description of the electromagnetic field. In section 21.2 we will depict specific experimenfs which have been performed fo show fhaf a quanfum description is necessary in some cases. We will describe in Section 21.3 fhe sfandard fools for fhe analysis of fhe sfafisfical properties of lighf and give fhe resulfs obfained for a number of sources. 

The free electron resides in a quantized energy well, defined by k (in wave-numbers). This result Ccm be derived from the Schroedinger wave-equation. However, in the presence of a periodic array of electromagnetic potentials arising from the atoms confined in a crystalline lattice, the energies of the electrons from all of the atoms are severely limited in orbit and are restricted to specific allowed energy bands. This potential originates from attraction and repulsion of the electron clouds from the periodic array of atoms in the structure. Solutions to this problem were... 

Photoelectric effect The effect produced when electromagnetic radiation knocks electrons out of a metal. Einstein used this phenomenon to show that light was quantized and came in energy packets called photons. 

When an electromagnetic wave interacts with resonators, the effect of quantization of all possible stationary stable oscillating amplitudes arises without the requirement of any specifically organized conditions (like the inhomogeneous action of external harmonic force). 

Finally, in the early 20th century Albert Einstein explained the photoelectric effect based on quantized packets of electromagnetic radiation called photons. These quickly led to the familiar relationships of the energy of a photon,... 

All spectra are due to the absorbance of electromagnetic radiation energy by a sample. Except for thermal (kinetic) energy, all other energy states of matter are quantized. Quantized transitions imply precise energy levels that would give rise to line spectra with virtually no line-width. Most spectral peaks have a definite width that can be explained in several ways. First, the spectral line-width can be related to the... 

The authors of Ref. [12] reconsidered the problem of magnetic field in quark matter taking into account the rotated electromagnetism . They came to the conclusion that magnetic field can exist in superconducting quark matter in any case, although it does not form a quantized vortex lattice, because it obeys sourceless Maxwell equations and there is no Meissner effect. In our opinion this latter result is incorrect, since the equations for gauge fields were not taken into account and the boundary conditions were not posed correctly. 

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