Modern Computational Methods
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Modern Physics with Modern Computational Methods
Modern Physics with Modern Computational Methods, Third Edition presents the ideas that have shaped modern physics and provides an introduction to current research in the different fields of physics. Intended as the text for a first course in modern physics following an introductory course in physics with calculus, the book begins with a brief and focused account of experiments that led to the formulation of the new quantum theory, while ensuing chapters go more deeply into the underlying physics.In this new edition, the differential equations that arise are converted into sets of linear equation or matrix equations by making a finite difference approximation of the derivatives or by using the spline collocation method. MATLAB programs are described for solving the eigenvalue equations for a particle in a finite well and the simple harmonic oscillator and for solving the radial equation for hydrogen. The lowest-lying solutions of these problems are plotted using MATLAB and the physical significance of these solutions are discussed.Each of the later chapters conclude with a description of modern developments. - Makes critical topics accessible by illustrating them with simple examples and figures - Presents modern quantum mechanical concepts systematically and applies them consistently throughout the book - Utilizes modern computational methods with MATLAB programs to solve the equations that arise in physics, and describes the programs and solutions in detail - Covers foundational topics, including transition probabilities, crystal structure, reciprocal lattices, and Bloch theorem to build understanding of applications, such as lasers and semiconductor devices - Features expanded exercises and problems at the end of each chapter as well as multiple appendices for quick reference
Aromaticity
Evaluating the aromaticity of a molecular system and the influence of this concept on its properties is a crucial step in the development of novel aromatic systems. Modern computational methods can provide researchers with a high level of insight into such aromaticity, but identifying the most appropriate method for assessing a specific system can prove difficult. Aromaticity: Modern Computational Methods and Applications reviews the latest state-of-the-art computational methods in this field and discusses their applicability for evaluating the aromaticity of a system. In addition to covering aromaticity for typical organic molecules, this volume also explores systems possessing transition metals in their structures, macrocycles and even transition structures. The influence of the aromaticity on the properties of these species (including the structure, magnetic properties and reactivity) is highlighted, along with potential applications in fields including materials science and medicinal chemistry. Finally, the controversial and fuzzy nature of aromaticity as a concept is discussed, providing the basis for an updated and more comprehensive definition of this concept. Drawing on the knowledge of an international team of experts, Aromaticity: Modern Computational Methods and Applications is a unique guide for anyone researching, studying or applying principles of aromaticity in their work, from computational and organic chemists to pharmaceutical and materials scientists. - Reviews a range of computational methods to assess the aromatic nature of different compounds, helping readers select the most useful tool for the system they are studying - Presents a complete guide to the key concepts and fundamental principles of aromaticity - Provides guidance on identifying which variables should be modified to tune the properties of an aromatic system for different potential applications
Computational Methods in Physics, Chemistry and Biology
Providing an accessible introduction to a range of modern computational techniques, this book is perfect for anyone with only a limited knowledge of physics. It leads readers through a series of examples, problems, and practical-based tasks covering the basics to more complex ideas and techniques. The focus is placed on the dynamic area of modern physics, helping readers understand the power and uses of computational physics. * Leads the reader from a basic introduction to more sophisticated techniques * Provides the skill-building exercises necessary to tackle more complex problems * Applies essential techniques to a wide range of key problems