Compton theory

Classical and Quantum Mechanics. At the beginning of the twentieth century, a revolution was brewing in the world of physics. For hundreds of years, the Newtonian laws of mechanics had satisfactorily provided explanations and supported experimental observations in the physical sciences. However, the experimentaUsts of the nineteenth century had begun delving into the world of matter at an atomic level. This led to unsatisfactory explanations of the observed patterns of behavior of electricity, light, and matter, and it was these inconsistencies which led Bohr, Compton, deBroghe, Einstein, Planck, and Schrn dinger to seek a new order, another level of theory, ie, quantum theory. 

Fig. 4-2. Continuous spectrum from a massive target obtained by superposition of spectra from thin targets. (After Compton and Allison, X-rays in Theory and Experiment D. Van Nostrand Co.)...

The Compton scattering cannot be neglected, but it is independent of molecular structure. Then, fitting experimental data to formulas from gas phase theory, the concentration of excited molecules can be determined. Another problem is that the undulator X-ray spectrum is not strictly monochromatic, but has a slightly asymmetric lineshape extending toward lower energies. This problem may be handled in different ways, for example, by approximating its spectral distribution by its first spectral moment [12]. 

Generally, all band theoretical calculations of momentum densities are based on the local-density approximation (LDA) [1] of density functional theory (DFT) [2], The LDA-based band theory can explain qualitatively the characteristics of overall shape and fine structures of the observed Compton profiles (CPs). However, the LDA calculation yields CPs which are higher than the experimental CPs at small momenta and lower at large momenta. Furthermore, the LDA computation always produces more pronounced fine structures which originate in the Fermi surface geometry and higher momentum components than those found in the experiments [3-5]. 

Experimental chemists are rarely concerned with quantum effects and it s not unusual to find them ignoring this fundamental theory altogether. Even when an effort is made to explore the topic more deeply traditional quantum phenomena like black-body radiation, Compton scattering and even the photoelectric effect may appear to be of somewhat limited importance. Experimentalists who rely on spectroscopic measurements get by with interpretations based on a few simple semi-classical rules, and without ever appreciating the deep significance of quantum theory. Maybe there is a problem with the rigorous mathematical formulation of quantum theory and too little emphasis on quantum effects routinely encountered in chemistry. 

Schrodinger s equation is widely known as a wave equation and the quantum formalism developed on the basis thereof is called wave mechanics. This terminology reflects historical developments in the theory of matter following various conjectures and experimental demonstration that matter and radiation alike, both exhibit wave-like and particle-like behaviour under appropriate conditions. The synthesis of quantum theory and a wave model was first achieved by De Broglie. By analogy with the dual character of light as revealed by the photoelectric effect and the incoherent Compton scattering... 

A broadening in Mark s intellect is shown clearly in his publications of this period. The topics in 1926 and 1927 alone ranged from atomic structure and quantum theory (1), and Compton radiation (2) to the scattering of x-rays by an ideal gas (3) and mineral structure (4). The shear diversity of his contacts and interests made him qualified for expanded responsibilities. 

Work on the structure of crystals and fibers was not the only way in which Mark made use of x-rays. With several collaborators, he reported the results of a number of significant investigations of the physics of x-rays in 1926 and 1927. With Ehrenberg he reported studies of the index of refraction of x-rays, and with Leo Szilard studies verifying the linear polarization of x-rays scattered from electrons at 90. An investigation of the width of x-ray lines was carried out by Mark and Ehrenberg, and Mark and Kallmann reported work on the properties of Compton-scattered x-radiation and on the theory of the dispersion and scattering of x-rays. 

There has been much quantitative work aimed at achieving agreement between theory and experimental isotropic Compton profiles. Particularly elaborate... 

Now we will briefly indicate the problems that can be usefully treated with the above geometric theory of the hydrogen atom." In many applications, such as the theory of the Compton effect in a bound electron and in the inelastic matter theory of atoms it is a question of determining the norm of the projection of a given function on the subspace of Hilbert space determined by the principal quanmni number nJ This norm is defined by the sum... 

Compton. R.G and Waller. A.M. (1988) in Speciroelectrochemisiry Theory and Practice, Gale, RJ. (ed.). Plenum Press, New York, Chapter 5. 

In this Physical Chemistry Primer, Tony Cox presents a clearly written, basic introduction to Quantum Theory—a subject which underpins the thinking behind all modem physical chemistry. The book explains in simple terms those basic ideas of quantum theory and its applications in describing the structure of atoms which are essential knowledge for any undergraduate chemist. This primer will be of interest to all students of chemistry (and their mentors). Richard G. Compton... 

The first inference of photon mass was made by Einstein and de Broglie on the assumption that the photon is a particle, and behaves as a particle in, for example, the Compton and photoelectric effects. The wave-particle duality of de Broglie is essentially an extension of the photon, as the quantum of energy, to the photon, as a particle with quantized momentum. The Beth experiment in 1936 showed that the photon has angular momentum, whose quantum is h. Other fundamental quanta of the photon are inferred in Ref. 42. In 1930, Proca [43] extended the Maxwell-Heaviside theory using the de Broglie guidance theorem ... 

Because quantum theory is supposed only to deal with observables it may be, and is, argued as meaningless to enquire into the internal structure of an electron, until it has been observed directly. To treat an electron as a point particle is therefore considered mathematically sufficient. However, an electron has experimentally observed properties such as the Compton wavelength and spin, which can hardly be ascribed to a point particle. The only reasonable account of such properties has, to date, been provided by wave models of the electron. 

Although the problem of the gross structure of cellulose is outside the scope of this review, it is of interest that Lieser32 has interpreted the behavior of cellulose with cuprammonium in support of a micellar theory of cellulose structure Staudinger,33 of a long chain theory Compton,34 of a particulate theory Hess,35 of a theory of secondary valence association between CsHioOs units and Pacsu,36 of a theory of acetal linkages in equidistant open-chain units and the laminated chain structure of cellulose. 

PHYSICAL PRINCIPLES OFTHEQUANTUMTHEORY. Werner Heisenberg. Nobel Laureate discusses quantum theory, uncertainty, wave mechanics, work of Dirac, Schroedinger, Compton, Wilson, Einstein, etc. 184pp. 5X x 8)4. 

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