Mathematical devices for optical sciences /

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"Version: 20190601"--Title page verso.Includes bibliographical references and index.1. Forms of quantum mechanics -- 1.1. The Schr?odinger and Heisenberg pictures -- 1.2. Interaction picture -- 1.3. Density-matrix formulation of quantum mechanics -- 1.4. Further contents of Heisenberg's commutation relations2. Lorentz group and its representations -- 2.1. Lie algebra of the Lorentz group -- 2.2. Two-by-two representation of the Lorentz group -- 2.3. Four-vectors in the two-by-two representation -- 2.4. Transformation properties in the two-by-two representation -- 2.5. Subgroups of the Lorentz group -- 2.6. Decompositions of the Sp(2) matrices -- 2.7. Bilinear conformal representation of the Lorentz group3. Internal space-time symmetries -- 3.1. Wigner's little groups -- 3.2. Little groups in the light-cone coordinate system -- 3.3. Two-by-two representation of the little groups -- 3.4. One expression with three branches -- 3.5. Classical damped oscillators4. Photons and neutrinos in the relativistic world of Maxwell and Wigner -- 4.1. The Lorentz group and Wigner's little groups -- 4.2. Massive and massless particles -- 4.3. Polarization of massless neutrinos -- 4.4. Scalars, vectors, tensors, and the polarization of photons5. Wigner functions -- 5.1. Basic properties of the Wigner phase-space distribution function -- 5.2. Time dependence of the Wigner function -- 5.3. Wave packet spread -- 5.4. Harmonic oscillators -- 5.5. Minimum uncertainty in phase space -- 5.6. Density matrix -- 5.7. Measurable quantities6. Coherent states of light -- 6.1. Phase-number uncertainty relation -- 6.2. Baker-Campbell-Hausdorff relation -- 6.3. Coherent states -- 6.4. Symmetry of coherent states -- 6.5. Coherent states in phase space -- 6.6. Single-mode squeezed states7. Squeezed states and their symmetries -- 7.1. Two-mode states -- 7.2. Unitary transformations -- 7.3. Symmetries of two-mode states -- 7.4. Dirac matrices and O(3,3) symmetry -- 7.5. Symmetries in phase space -- 7.6. Two coupled oscillators8. Entanglement and entropy -- 8.1. Density matrix and entropy -- 8.2. Two-by-two density matrices -- 8.3. Density matrix for two-oscillator states -- 8.4. Entropy for the two-mode state -- 8.5. Entangled excited states -- 8.6. Wigner functions and uncertainty relations9. Ray optics and optical activities -- 9.1. Ray optics using the group of ABCD matrices -- 9.2. Physical examples using ABCD matrices -- 9.3. Optical activities10. Polarization optics -- 10.1. Jones vector, phase shifters, and attenuators -- 10.2. New filters and possible applications -- 10.3. Non-orthogonal coordinate systems -- 11. Stokes parameters and Poincar?e sphere -- 11.1. Polarization optics and decoherence -- 11.2. Coherency matrix and Stokes parameters -- 11.3. Poincar?e sphere -- 11.4. The entropy problem -- 11.5. Further symmetries from the Poincar?e sphereAppendix A. Covariant harmonic oscillators and the quark-parton puzzle -- A.1. The covariant harmonic oscillator -- A.2. Quark-parton puzzle.The Lorentz group which is the underlying scientific language for modern optics has been most notably used for understanding Einstein's special relativity. By using a simplified approach of two-by-two matrices and Wigner functions, this book provides a basic and novel approach to classical and quantum optics, making these often-difficult subjects more transparent to the reader. Written by three experts in the field, Professors Sibel Ba?skal, Young S. Kim, and Marilyn E Noz, this book will give the reader a comprehensive overview of how fundamental issues in quantum mechanics can be approached using various optical instruments, Wigner functions, and quantum entanglement.Students, researchers and practitioners interested in developing new theories for quantum mechanics and information theory.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Professor Young S. Kim graduated from Princeton University in 1961 and has been a faculty member of the University of Maryland since 1962. As a well-respected and extremely learned physicist, he has published numerous works throughout his extensive career and continues to work closely with pupils and colleagues as well as continuing his own research in particle theory, quantum mechanics, and further contents of Einstein's work. Professor Sibel Ba?skal is Physics Professor at the Middle East Technical University. She is particularly interested in the manifestations of the Poincar?e and little groups, and of group contractions in physical sciences. Her research interests extend to current problems in classical field theories, mostly on alternative approaches to Einstein's gravity. She has published more than 30 peer-reviewed papers and is the co-author of two books with Y.S. Kim and M.E. Noz. Professor Marilyn E. Noz is Professor Emerita in the Department of Radiology at NYU School of Medicine. Over the last more than 40 years, she has collaborated with Professor Kim on relativistic quantum mechanics using two-by-two matrices, harmonics oscillators, and the Lorentz group. She has contributed to over 40 peer-reviewed journal articles in elementary particle physics and optics. She has written three books with Professor Kim and two books with Professors Kim and Ba?skal. She continues to do research in elementary particle physics and quantum optics.Title from PDF title page (viewed on July 2, 2019).

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: .,

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1 online resource (various pagings) :illustrations (chiefly color).

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English

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9780750316149

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535.0151

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SCIENCE / Physics / Mathematical & Computational.
Mathematical physics.
Optics
Quantum optics.

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Sibel Ba?skal, Young S. Kim, Marilyn E. Noz.

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