PRINCIPLES OF QUANTUM MECHANICS (2版)
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【原文書】
書名：Principles of Quantum Mechanics 2/e
作者:R. Shankar
出版社：Kluwer Academic Plenum Publishers
ISBN：9780306447907
About this Textbook
Reviews from the First Edition:
"An excellent text … The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner." (American Scientist)
"No matter how gently one introduces students to the concept of Dirac’s bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of." (Physics Bulletin)
Reviews of the Second Edition:
"This massive text of 700 and odd pages has indeed an excellent get-up, is very verbal and expressive, and has extensively worked out calculational details---all just right for a first course. The style is conversational, more like a corridor talk or lecture notes, though arranged as a text. … It would be particularly useful to beginning students and those in allied areas like quantum chemistry." (Mathematical Reviews)
R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include:
- Clear, accessible treatment of underlying mathematics
- A review of Newtonian, Lagrangian, and Hamiltonian mechanics
- Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates
- Unsurpassed coverage of path integrals and their relevance in contemporary physics
The requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book’s self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.
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Fractional Partial Differential Equations
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【簡介】
This monograph offers a comprehensive exposition of the theory surrounding time-fractional partial differential equations, featuring recent advancements in fundamental techniques and results. The topics covered encompass crucial aspects of the theory, such as well-posedness, regularity, approximation, and optimal control. The book delves into the intricacies of fractional Navier–Stokes equations, fractional Rayleigh–Stokes equations, fractional Fokker–Planck equations, and fractional Schrödinger equations, providing a thorough exploration of these subjects. Numerous real-world applications associated with these equations are meticulously examined, enhancing the practical relevance of the presented concepts.
The content in this monograph is based on the research works carried out by the author and other excellent experts during the past five years. Rooted in the latest advancements, it not only serves as a valuable resource for understanding the theoretical foundations but also lays the groundwork for delving deeper into the subject and navigating the extensive research landscape. Geared towards researchers, graduate students, and PhD scholars specializing in differential equations, applied analysis, and related research domains, this monograph facilitates a nuanced understanding of time-fractional partial differential equations and their broader implications.
【目錄】
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FRACTIONAL DISCRETE CHAOS
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In the nineteenth-century, fractional calculus had its origin in extending differentiation and integration operators from the integer-order case to the fractional-order case. Discrete fractional calculus has recently become an important research topic, useful in various science and engineering applications. The first definition of the fractional-order discrete-time/difference operator was introduced in 1974 by Diaz and Osler, where such operator was derived by discretizing the fractional-order continuous-time operator. Successfully, several types of fractional-order difference operators have then been proposed and introduced through further generalizing numerous classical operators, motivating several researchers to publish extensively on a new class of systems, viz the nonlinear fractional-order discrete-time systems (or simply, the fractional-order maps), and their chaotic behaviors. This discovery of chaos in such maps, has led to novel control methods for effectively stabilizing their chaotic dynamics.
The aims of this book are as follows:
Presenting the recent developments, trends, research solutions, applications and open problems related to fractional-order chaotic maps;
Illustrating many interdisciplinary applications, like modulization, control, circuits, security and encryption;
Including all theories associated with chaos, control and synchronization of discrete-time systems;
Providing a useful reference on the topic of fractional-order chaotic maps and their applications.
Sample Chapter(s)
Preface
Chapter 1: Discrete Fractional Calculus
Contents:
Discrete Fractional Calculus
Chaotic Methods and Tests
Chaos in 2D Discrete Fractional Systems
Chaos in 3D Discrete Fractional Systems
Applications of Fractional Chaotic Maps
Readership: Graduate students and researchers in chaos, applied mathematics, computer science and engineering.
原價:
2411
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2290
現省:
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Numerical Treatment and Analysis of Time-Fractional Evolution Equations
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SPECIAL FUNCTIONS OF FRACTIONAL CALCULUS
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This book aims to provide an overview of the special functions of fractional calculus and their applications in diffusion and random search processes. The book contains detailed calculations for various examples of anomalous diffusion, random search and stochastic resetting processes, which can be easily followed by the reader, who will be able to reproduce the obtained results. The book will be intended for advanced undergraduate and graduate students and researchers in physics, mathematics and other natural sciences due to the various examples which will be provided in the book.
Sample Chapter(s)
Preface
Chapter 1: Mathematical background
Contents:
Mathematical Background
Fox H-Function and Related Functions
Elements of Random Walk Theory
CTRW on Combs
Heterogeneous Diffusion Processes
Diffusion Processes with Stochastic Resetting
Random Search
Diffusion on Fractal Tartan
Finite-Velocity Diffusion
Appendices:
Functional Calculus Stochastic Differential Equations Large Deviation Principle Fractals and Fractal Dimension Implementation of Wolfram Mathematica
Readership: Advanced undergraduate and graduate students, researchers in the fields of stochastic processes, fractional calculus, anomalous diffusion, random search, stochastic resetting, econophysics.
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Fractional Differential Equations 2021 <SV>
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