Classical waves electromagnetic radiation theory

We shall apply the time-dependent perturbation theory of the last section to a system exposed to electromagnetic radiation. Before doing so, we review the classical wave theory of light.2... 

We now consider the effect of exposing a system to electromagnetic radiation. Our treatment will involve approximations beyond that of replacing (3.13) with (3.16). A proper treatment of the interaction of radiation with matter must treat both the atom and the radiation field quantum-mechanically this gives what is called quantum field theory (or quantum electrodynamics). However, the quantum theory of radiation is beyond the scope of this book. We will treat the atom quantum-mechanically, but will treat the radiation field as a classical wave, ignoring its photon aspect. Thus our treatment is semiclassical. 

THE PHYSICS OF WAVES, William C. Elmore and Mark A. Heald. Unique overview of classical wave theory. Acoustics, optics, electromagnetic radiation, more. Ideal as classroom text or for self-study. Problems. 477pp. 5b 8b. 

We begin by discussing the transition from classical physics to quantum theory. In particular, we become familiar with properties of waves and electromagnetic radiation and Planck s formulation of the quantum theory. (7.1)... 

Classical physics just before 1900 consisted of two major theoretical frameworks. The first was classical mechanics, which seeks to explain the motion of matter, and the second was the wave theory of light, a description of electromagnetic radiation. 

The classical theory of electromagnetic radiation, attributed primarily to James Clerk Maxwell, describes radio waves, microwaves, infrared and visible and ultraviolet light, x-rays, and y-rays all as combinations of oscillating... 

Maxwell s equations describe the propagation of electromagnetic radiation as waves within the framework of classical physics however, they do not describe emission phenomena. The search for the law that defines the energy distribution of radiation from a small hole in a large isothermal cavity gave rise to quantum theory. The function that describes the frequency distribution of blackbody radiation was the first result of that new theory (Planck, 1900,1901). 

These observations, especially the dependency on frequency, could not be explained by classical wave theory. However, Albert Einstein showed that they are exactly what would be expected with a particle interpretation of radiation. In 1905, Einstein proposed that electromagnetic radiation has particle-like... 

In 1913 Niels Bohr proposed a system of rules that defined a specific set of discrete orbits for the electrons of an atom with a given atomic number. These rules required the electrons to exist only in these orbits, so that they did not radiate energy continuously as in classical electromagnetism. This model was extended first by Sommerfeld and then by Goudsmit and Uhlenbeck. In 1925 Heisenberg, and in 1926 Schrn dinger, proposed a matrix or wave mechanics theory that has developed into quantum mechanics, in which all of these properties are included. In this theory the state of the electron is described by a wave function from which the electron s properties can be deduced. 

By definition, the atomic scattering factor /(x) is given in terms of the amplitude scattered by a single electron at the lattice point. It is useful, however, to have the scattered amplitude/I in terms of the incident amplitude Aq. From classical electromagnetic theory, it follows that if a wave of amplitude Aq is incident on a free electron, the amplitude A of the radiation emitted in the forward direction, at a distance R (meters) from the electron, is given by... 

A familiar device in modem technology is the photocell or electric eye, which mns a variety of useful gadgets, including automatic door openers. The principle involved in these devices is the photoelectric effect, which was first observed by Heinrich Hertz in the same laboratory in which he discovered electromagnetic waves. Visible or ultraviolet radiation impinging on clean metal surfaces can cause electrons to be ejected from the metal. Such an effect is not, in itself, inconsistent with classical theory since electromagnetic waves are known to carry energy and momentum. But the detailed behavior as a function of radiation frequency and intensity cannot be explained classically. 

All the considerations that follow are only valid for radiation that is stimulated thermally. Radiation is released from all bodies and is dependent on their material properties and temperature. This is known as heat or thermal radiation. Two theories are available for the description of the emission, transfer and absorption of radiative energy the classical theory of electromagnetic waves and the quantum theory of photons. These theories are not exclusive of each other but instead supplement each other by the fact that each describes individual aspects of thermal radiation very well. 

Here, h = (6.626 068 76 0.000 000 52)-10 34 Js is the Planck constant, also known as Planck s action quantum v is the frequency of the photons. Quantum theory is required to calculate the spectral distribution of the energy emitted by a body. Other aspects of heat transfer can, in contrast, be covered by classical theory, according to which the radiation is described as the emission and propagation of electromagnetic waves. 

In view of the experimental difficulties a theory for radiation properties is desirable. The classical theory of electromagnetic waves from J.C. Maxwell (1864), links the emissivity e x with the so-called optical constants of the material, the refractive index n and the extinction coefficient k, that can be combined into a complex refractive index n = n — ik. The optical constants depend on the temperature, the wavelength and electrical properties, in particular the electrical resistivity re of the material. In addition, the theory delivers, in the form of Fresnel s equations, an explicit dependence of the emissivity on the polar angle / , whilst no dependence on the circumferential angle ip appears, as isotropy has been assumed. 

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