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Author: H. E. Moses
Publisher:
Published: 1972
Total Pages: 60
ISBN-13:
DOWNLOAD EBOOKAuthor: Air Force Cambridge Research Laboratories (U.S.)
Publisher:
Published: 1972
Total Pages: 214
ISBN-13:
DOWNLOAD EBOOKThis bibliography lists all AFCRL in-house reports, journal articles, and contractor reports issued from 1 January to 31 March 1972. Abstracts are included.
Author: Harry E. Moses
Publisher:
Published: 1972
Total Pages: 70
ISBN-13:
DOWNLOAD EBOOKThe expansion of the unquantized electromagnetic fields and vector and scalar potentials in terms of the wave functions of the relativistic photon is reviewed and extended. Both linear and angular momentum bases are used for the photon wave functions. After second quantizing the electromagnetic field, the results are applied to the obtaining of the exact matrix elements (that is, with retardation taken into account exactly) and selection rules for the emission of photons by hydrogenic atoms. The dichotomy between the photon and wave picture of electromagnetic radiation is discussed and resolved. Furthermore, the most general vector and scaler potentials are obtained through the use of the eigenfunctions of the curl operator. (Author).
Author: Air Force Cambridge Research Laboratories (U.S.)
Publisher:
Published: 1972
Total Pages: 336
ISBN-13:
DOWNLOAD EBOOKAuthor: Air Force Cambridge Research Laboratories (U.S.)
Publisher:
Published: 1971
Total Pages: 180
ISBN-13:
DOWNLOAD EBOOKThis bibliography lists all AFCRL in-house reports, journal articles, and contractor reports issued from 1 July to 30 September 1971. Abstracts are included.
Author: Air Force Cambridge Research Laboratories (U.S.)
Publisher:
Published: 1972
Total Pages: 212
ISBN-13:
DOWNLOAD EBOOKThis bibliography lists all AFCRL in-house reports, journal articles, and contractor reports issued during the reporting period. The DD Form 1473 (Document Control Data - R & D) for each publication is included. In Part I, the 1473's for in-house reports are arranged numerically by the series in which they were issued: in Part II, the 1473's for journal articles are arranged alphabetically by author; in Part III, the 1473's for contractor reports are arranged alphabetically by corporate author. For cross-reference purposes, an index is included, listing the publications numerically by the AFCRL document number.
Author: Harry E. Moses
Publisher:
Published: 1973
Total Pages: 38
ISBN-13:
DOWNLOAD EBOOKConsideration is given to the problem of the scattering of a photon by hydrogen in the ground state when the photon has its principal frequencies near that of Lyman-alpha radiation. The scattering operator and cross-section is obtained for this process. The procedure is to adapt Dirac's theory of resonance scattering to the problem and, by quantizing the electromagnetic field in an angular momentum basis, to solve the problem exactly within the framework of the Dirac theory. The total scattering cross-section at resonance is found to be 7.062 x 10 to the -12th power sq. cm. The natural half width of the scattered line is 0.000103 A. The resonance frequency itself is shifted toward the long wave length side by 4281 mc/sec. The shift in the resonance from the original Lyman-alpha frequency can be interpreted as an indication that the Dirac resonance scattering theory contains a large part of the Lamb shift of the ground state. This fact suggests new ways of obtaining the Lamb shift for various levels which will be explored later. (Author).
Author: Harry E. Moses
Publisher:
Published: 1973
Total Pages: 28
ISBN-13:
DOWNLOAD EBOOKJust as one uses the power spectrum of the Fourier transform of data given as a function of a one-dimensional variable to find periodicities in the translation of the variable, one may use the power spectrum of the Mellin transform to find periodicities in the magnification. The relation of the Fourier transform to the Mellin transform is discussed, and a theorem of the Wiener-Khinchine type is presented. The use of the Mellin transform, offers a new method of extracting meaningful features from data, particularly when the data is noisy.
Author: Gregory S. Chirikjian
Publisher: CRC Press
Published: 2021-02-25
Total Pages: 697
ISBN-13: 1000694259
DOWNLOAD EBOOKFirst published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.
