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Computational spectroscopy and computational quantum chemical dynamics is a vast field in physical chemistry. Significant part of this field is developed based on the concepts of time-dependent quantum mechanics and its numerical implementations.This book gives an introduction to the Time-Dependent Quantum Chemistry for use with any introductory college/university course in optics, spectroscopy, kinetics, dynamics, or experimental physical chemistry or chemical physics of the kind usually taken by undergraduate and graduate students in physical chemistry. In this book, different concepts of time-dependent quantum mechanics are systematically presented by first giving emphasis on the contrasting viewpoint of classical and quantum mechanical motion of a particle, then by demonstrating the ways to find classical flavour in quantum dynamics, thereafter by formally defining the wavepacket which represents a quantum particle and finally by demonstrating numerical methods to explore the wavepacket dynamics in one dimension. Along with the analytical theory, accompanying Python chapters in this book take readers to a hands-on tour with Python programming by first giving them a quick introduction to the Python programming, then by introducing the position-space grid representation of the wavefunction, thereafter, by making them familiarized with the Fourier transform to represent the discretized wavefunction in momentum space, subsequently by showing the Python-based methodologies to express Hamiltonian operator in matrix form and finally by demonstrating the entire Python program which solves the wavepacket dynamics in one dimension under influence of time-independent Hamiltonian following split-operator approach.Rigorous class-testing of the presented lecture notes at the Indian Institute of Science, GITAM University and at NPTEL platform reveals that physical chemistry students, after thoroughly going through all chapters, not only develop an in-depth understanding of the wavepacket dynamics and its numerical implementations, but also start successfully writing their own Python code for solving any one dimensional wavepacket dynamics problem.
Computational spectroscopy and computational quantum chemical dynamics is a vast field in physical chemistry. Significant part of this field is developed based on the concepts of time-dependent quantum mechanics and its numerical implementations. This book gives an introduction to the Time-Dependent Quantum Chemistry for use with any introductory college/university course in optics, spectroscopy, kinetics, dynamics, or experimental physical chemistry or chemical physics of the kind usually taken by undergraduate and graduate students in physical chemistry. In this book, different concepts of time-dependent quantum mechanics are systematically presented by first giving emphasis on the contrasting viewpoint of classical and quantum mechanical motion of a particle, then by demonstrating the ways to find classical flavour in quantum dynamics, thereafter by formally defining the wavepacket which represents a quantum particle and finally by demonstrating numerical methods to explore the wavepacket dynamics in one dimension. Along with the analytical theory, accompanying Python chapters in this book take readers to a hands-on tour with Python programming by first giving them a quick introduction to the Python programming, then by introducing the position-space grid representation of the wavefunction, thereafter, by making them familiarized with the Fourier transform to represent the discretized wavefunction in momentum space, subsequently by showing the Python-based methodologies to express Hamiltonian operator in matrix form and finally by demonstrating the entire Python program which solves the wavepacket dynamics in one dimension under influence of time-independent Hamiltonian following split-operator approach. Rigorous class-testing of the presented lecture notes at the Indian Institute of Science, GITAM University and at NPTEL platform reveals that physical chemistry students, after thoroughly going through all chapters, not only develop an in-depth understanding of the wavepacket dynamics and its numerical implementations, but also start successfully writing their own Python code for solving any one dimensional wavepacket dynamics problem.
This unique compendium stresses on physical concepts and the applications to practical problems. The authors' decades of experience in teaching, research and industrial consultancy are reflected in the choice of the solved examples and unsolved problems.The second edition has three additional chapters containing topics of vibration and acoustic sensors and instruments, finite element method (FEM), boundary element method (BEM) and statistical energy analysis (SEA), etc, thus enabling students to solve real-life problems in industrial and automotive noise control.The useful reference text targets senior undergraduate mechanical and environmental engineering students as well as designers of industrial machinery and layouts. The book can readily be used for self-study by practicing designers and engineers. Mathematical derivations are avoided and illustrations, tables and empirical formulae are included for ready reference.
Quantum mechanics undergraduate courses mostly focus on systems with known analytical solutions; the finite well, simple Harmonic, and spherical potentials. However, most problems in quantum mechanics cannot be solved analytically. This textbook introduces the numerical techniques required to tackle problems in quantum mechanics, providing numerous examples en route. No programming knowledge is required – an introduction to both Fortran and Python is included, with code examples throughout. With a hands-on approach, numerical techniques covered in this book include differentiation and integration, ordinary and differential equations, linear algebra, and the Fourier transform. By completion of this book, the reader will be armed to solve the Schrödinger equation for arbitrarily complex potentials, and for single and multi-electron systems.
Computational Modeling, by Jay Wang introduces computational modeling and visualization of physical systems that are commonly found in physics and related areas. The authors begin with a framework that integrates model building, algorithm development, and data visualization for problem solving via scientific computing. Through carefully selected problems, methods, and projects, the reader is guided to learning and discovery by actively doing rather than just knowing physics.
This introductory book is aimed at students of engineering and material science who want to learn the necessary toolboxes of practical quantum mechanics. The authors have made sure that all the calculations are complete, and they have avoided the usage of the familiar phrase, 'it can be easily shown' while being mathematically rigorous. Knowledge of the sophomore level introduction to ordinary differential equations is all that is needed. Well-designed and modern examples help the reader grasp and digest the concept before moving to the next one. The book offers a lucid exposition to the modern field of quantum computing and quantum gates, two-level systems, orbitals, spin, periodic solids, tunneling, and Fermi golden rule. The basics of electronic and optical properties of nanomaterials using the basics of quantum mechanics are presented without the reader getting lost in research articles with different notations and units.There are numerous examples in the book covering topics such as carbon nanotubes, graphene, superconducting qubits, principle of scanning tunneling microscopy, heterostructure based terahertz generation and negative differential resistance device, quantized LC circuit, Grover's search algorithm, phase kickback, quantum dots, well, nanowires, quantum of conductance, ballistic conductor, spin-orbit coupling, and spin transistor. Authors use analogies based on familiar engineering concepts wherever possible to broaden the view of the reader. The philosophy behind the book is teaching by showing how it is done and using 'pictures' which is worth 1000 words.
The use of parallel programming and architectures is essential for simulating and solving problems in modern computational practice. There has been rapid progress in microprocessor architecture, interconnection technology and software devel- ment, which are in?uencing directly the rapid growth of parallel and distributed computing. However, in order to make these bene?ts usable in practice, this dev- opment must be accompanied by progress in the design, analysis and application aspects of parallel algorithms. In particular, new approaches from parallel num- ics are important for solving complex computational problems on parallel and/or distributed systems. The contributions to this book are focused on topics most concerned in the trends of today’s parallel computing. These range from parallel algorithmics, progr- ming, tools, network computing to future parallel computing. Particular attention is paid to parallel numerics: linear algebra, differential equations, numerical integ- tion, number theory and their applications in computer simulations, which together form the kernel of the monograph. We expect that the book will be of interest to scientists working on parallel computing, doctoral students, teachers, engineers and mathematicians dealing with numerical applications and computer simulations of natural phenomena.
Our future scientists and professionals must be conversant in computational techniques. In order to facilitate integration of computer methods into existing physics courses, this textbook offers a large number of worked examples and problems with fully guided solutions in Python as well as other languages (Mathematica, Java, C, Fortran, and Maple). It’s also intended as a self-study guide for learning how to use computer methods in physics. The authors include an introductory chapter on numerical tools and indication of computational and physics difficulty level for each problem. Readers also benefit from the following features: • Detailed explanations and solutions in various coding languages. • Problems are ranked based on computational and physics difficulty. • Basics of numerical methods covered in an introductory chapter. • Programming guidance via flowcharts and pseudocode. Rubin Landau is a Distinguished Professor Emeritus in the Department of Physics at Oregon State University in Corvallis and a Fellow of the American Physical Society (Division of Computational Physics). Manuel Jose Paez-Mejia is a Professor of Physics at Universidad de Antioquia in Medellín, Colombia.
This advanced textbook provides an introduction to the basic methods of computational physics.