Quantization of radiation

Quantization of radiation field in terms of field intensity operators, 562 Quantum electrodynamics, 642 asymptotic condition, 698 gauge invariance in relation to operators inducing inhomogeneous Lorentz transformations, 678 invariance properties, 664 invariance under discrete transformations, 679... 

To conclude this introduction to quantum mechanics, it is interesting to note the omnipresence and the agglutinating role of Planck s constant. Indeed, if it was set equal to zero, all the construction which began with black-body radiation and the quantization of radiation energy, followed by the wave-matter duality and the Heisenberg principle. .. would fall down. In addition, the intrinsic angular momentum (spin) of some particles, including the electron, would be forced to be zero, with many consequences at the theoretical and practical levels. 

Fundamental noise or random noise this type of noise is statistically distributed and its amplitude as a function of the frequency can be written as a sum of many sinusoidal functions. This type of noise is related to the corpuscular nature of matter or to the quantization of radiation, respectively, and cannot be completely eliminated. 

Chemistry students are familiar with spectrophotometry, the qualitative and quantitative uses of which are widespread in contemporary chemistry. The various features of absorption spectra are due to the absorption of radiation to promote a particle from one quantized energy state to another. The scattering phenomena we discuss in this chapter are of totally different origin classical not quantum physics. However, because of the relatively greater familiarity of absorption spectra, a comparison between absorption and scattering is an appropriate place to begin our discussion. 

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. 

The word LASER is an acronym for Light Amplification by Stimulated Emission of Radiation. The physical process upon which lasers depend, stimulated emission, was first elucidated by Einstein in 1917 (1). Einstein showed that in quantized systems three processes involving photons must exist absorption, spontaneous emission, and stimulated emission. These may be represented as follows ... 

Not really a spectroscopic technique in that the line spectrum produced does not arise from quantization of electromagnetic radiation. Of specialized interest only not further discussed here. 

Electron Motion Around the Nucleus. The first approach to a treatment of these problems was made by Niels Bohr in 1913 when he formulated and applied rules for quantization of electron motion around the nucleus. Bohr postulated states of motion of the electron, satisfying these quantum rules, as peculiarly stable. In fact, one of them would be really permanently stable and would represent the ground state of the atom, The others would be only approximately stable. Occasionally an atom would leave one such state for another and, in the process, would radiate light of a frequency proportional to the difference in energy between the two states. By this means, Bohr was able to account for the spectrum of atomic hydrogen in a spectacular way. Bohr s paper in 1913 may well be said to have set the course of atomic physics on its latest path. 

The problem of specific heats, treated by Jeans from the classical point of view, as I said above, was discussed by Einstein in the case of solids, with special regard to the discrepancy observed at low temperature between the measured values and those deduced from the theory he had constructed in 1907 by quantizing the mechanical oscillators3 as Planck had quantized the radiation oscillators. 

There are several reasons for starting this account with a discussion of electromagnetic radiation. Historically, it was in this area that the quantum theory first developed. It is easier here to understand the evidence for the theory, and to appreciate some of its paradoxical consequences, than it is in the quantum theory of matter. The applications of the light-quantum hypothesis, as it was first called, also provide key pieces of evidence for the quantization of energy in atoms and molecules. Studies of the absorption and emission of radiation—the field of spectroscopy—and of the effect of light on chemical reactions—photochemistry—are very important areas of modem chemistry, in which the quantum nature of radiation is crucial. 

Most other forms of spectroscopy do not involve emission of extra particles such as electrons, but the straightforward absorption or emission of photons. These processes increase or decrease the energy of an atom ex molecule, by an amount equal to the photon energy. The results all reinforce the conclusion of photoelectron spectroscopy that only discrete energy levels occur (see Fig. 1.12). For example, the line spectra of atoms, known since the early nineteenth century, only contain lines at certain well-defined wavelengths. The quantization of energy, not only in electromagnetic radiation but in material systems, is an inescapable conclusion rtf spectroscopy. 

The B cyclic theorem is a Lorentz invariant construct in the vacuum and is a relation between angular momentum generators [42], As such, it can be used as the starting point for a new type of quantization of electromagnetic radiation, based on quantization of angular momentum operators. This method shares none of the drawbacks of canonical quantization [46], and gives photon creation and annihilation operators self-consistently. It is seen from the B cyclic theorem ... 

Energy of radiation is quantized in photons, e = hv one photon excites one molecule to a higher energy state. 

Gamut constraint 2D Described in Section 6.5. If an empty intersection is created, the convex hulls are increased by a small amount. This process is repeated until a nonempty intersection is achieved. A histogram quantization of 256 per channel is used. Illuminants were constrained to lie on the curve of the black-body radiator. (Caliblmage= )... 

Two papers by Albert Einstein ultimately led to acceptance of the idea of quantization of energy for radiation, and were central to the development of the quantum theory (ironically, in later years Einstein became the most implacable critic of this same theory). The first of these papers, in 1905, concerned the photoelectric effect. Light ejected electrons from a metallic surface if the light had a greater frequency than some threshold frequency v0 which depended on the particular metal. The kinetic energy K of the emitted electrons was proportional to the excess frequency, v — v0 (Figure 5.4). Only the number of emitted electrons, not the kinetic energy, increased as the intensity increased. 

The main objection against the Bohr and Sommerfeld atomic models was the ad hoc definition of stationary states. Simply declaring these as quantum states offers no explanation for the failure of an accelerated charge to radiate energy. The quantization of neither energy nor angular momentum implies such an effect. 

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