A Comprehensive Guide to Angular Momentum begins by considering substantiations of the theorem of angular momentum change and the law of conservation of angular momentum, as the change of angular momentum indicates an error in the method of calculating the dynamics of the Solar system. Following this, different techniques for the analysis of the orbital angular momentum of electromagnetic fields are reviewed and discussed, describing their main advantages and disadvantages, and providing key ready-to-use methods for detection. The concluding chapter provides a theoretical explanation of photonic orbital angular momentum and explains its distinction from atomic orbital angular momentum. Global conservation of angular momentum implies that light must transfer not only its spin, but also its orbital angular momentum in order to matter.

Develops angular momentum theory in a pedagogically consistent way, starting from the geometrical concept of rotational invariance. Uses modern notation and terminology in an algebraic approach to derivations. Each chapter includes examples of applications of angular momentum theory to subjects of current interest and to demonstrate the connections between various scientific fields which are provided through rotations. Includes Mathematica and C language programs.

This book offers a concise introduction to the angular momentum, one of the most fundamental quantities in all of quantum mechanics. Beginning with the quantization of angular momentum, spin angular momentum, and the orbital angular momentum, the author goes on to discuss the Clebsch-Gordan coefficients for a two-component system. After developing the necessary mathematics, specifically spherical tensors and tensor operators, the author then investigates the 3-j, 6-j, and 9-j symbols. Throughout, the author provides practical applications to atomic, molecular, and nuclear physics. These include partial-wave expansions, the emission and absorption of particles, the proton and electron quadrupole moment, matrix element calculation in practice, and the properties of the symmetrical top molecule.

Science and Faith Can—and Do—Support Each Other Science and Christianity are often presented as opposites, when in fact the order of the universe and the complexity of life powerfully testify to intelligent design. With this comprehensive resource that includes the latest research, you’ll witness how the findings of scientists provide compelling reasons to acknowledge the mind and presence of a creator. Featuring more than 45 entries by top-caliber experts, you’ll better understand… how scientific concepts like intelligent design are supported by evidence the scientific findings that support the history and accounts found in the Bible the biases that lead to scientific information being presented as a challenge—rather than a complement—to Christianity Whether you’re looking for answers to your own questions or seeking to explain the case for intelligent design to others, The Comprehensive Guide to Science and Faith is an invaluable apologetic tool that will help you explore and analyze the relevant facts, research, and theories in light of biblical truth.

Table of Contents Mathematical Preliminaries Determinants and Matrices Vector Analysis Tensors and Differential Forms Vector Spaces Eigenvalue Problems Ordinary Differential Equations Partial Differential Equations Green's Functions Complex Variable Theory Further Topics in Analysis Gamma Function Bessel Functions Legendre Functions Angular Momentum Group Theory More Special Functions Fourier Series Integral Transforms Periodic Systems Integral Equations Mathieu Functions Calculus of Variations Probability and Statistics.

Designed as a learning tool for those with limited background in quantum mechanics, this book provides comprehensive coverage of angular momentum in quantum mechanics and its applications to chemistry and physics. Based on class-tested material, this presentation offers clear explanations of theory while giving equal attention to solving real problems. Theoretical considerations are made concrete and accessible through extensive examples and applications at the end of each chapter. Problem sets, designed as both individual and group exercises, are treated as an integral part of the text in order to stimulate student interest and clarify the abstract principles discussed. Examples are drawn primarily from atomic and molecular phenomena, and include many intermediate steps (often left out of other texts) to ensure complete mastery of the material, and to lay the groundwork for understanding photon and particle collision phenomena, and more advanced studies.

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