Quantum Mechanics: Volume 3: Lectures on Theoretical Physics (1版)

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【簡介】 The universe we live in is both strange and interesting. This strangeness comes about because, at the most fundamental level, the universe is governed by the laws of quantum mechanics. This is the most spectacularly accurate and powerful theory ever devised, one that has given us insights into many aspects of the world, from the structure of matter to the meaning of information. This textbook provides a comprehensive account of all things quantum. It starts by introducing the wavefunction and its interpretation as an ephemeral wave of complex probability, before delving into the mathematical formalism of quantum mechanics and exploring its diverse applications, from atomic physics and scattering, to quantum computing. Designed to be accessible, this volume is suitable for both students and researchers, beginning with the basics before progressing to more advanced topics.

Elementary Quantum Mechanics: With Problems and Solutions (1版)

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【簡介】 The impact of quantum mechanics on our day-to-day life is growing at an exponential rate, of which most people are unaware. For example, the toaster is a prime example of a quantum mechanical device. While quantum mechanics arose as a subject in physics, quantum mechanical thinking has had, and continues to have, a broad impact on mathematics. For example, operator theory as we know it today would not exist without von Neumann’s effort to put quantum mechanics on a solid mathematical foundation. This book is defined for undergraduate students of mathematics to obtain an introduction to quantum mechanical ideas, and the associated mathematics, without requiring an extensive background in physics.This book is focused around the following topics. 1) The Mathematical Structure of Quantum Mechanics. We develop the main mathematical structure of quantum theory in the setting of the accepted postulates of quantum mechanics. Dirac’s bra-ket notation for the required linear algebra aspects will be utilized, as well as the mathematical and physical implications arising from the mathematical aspects of self-adjoint linear operators, with emphasis on the finite dimensional setting. 2) Dynamics of a Quantum Particle. We introduce the Schrodinger equation and discuss its physical meaning and mathematical structure. The required partial differential equations theory is elementary, and will be developed from scratch. 3) Measurement, Time Evolution, Uncertainty, and the Harmonic Oscillator. This builds on the previously developed mathematics and culminates with a detailed discussion of the quantum mechanical workhorse example - the harmonic oscillator. 4) Quantum Mechanics of Angular Momentum. Most of the book is developed in the context of the (relatively) simple one dimensional quantum systems. This topic goes into three dimensions and illustrates how very interesting mathematics can yield novel physical explanations that are unobtainable with classical methods. 5) The Postulates of Quantum Mechanics, Measurement, Composite Systems, Tensor Products, and Entanglement. This is the area that most students have heard of - quantum entanglement, ＂action-at-a- distance＂ and Bell’s inequality. The mathematics will be at an elementary level (except possibly for tensor products, which are sadly neglected many linear algebra courses today, but which are literally exploding in a variety of current applications).

JOHN D. JACKSON - A COURSE IN QUANTUM MECHANICS (1版)

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【簡介】 【目錄】 1 Basics 2 Reformulation 3 Wentzel-Kramers-Brillouin (WKB) Method 4 Rotations, Angular Momentum, and Central Force Motion 5 Time-Independent Perturbation Theory 6 Atomic Structure 7 Time-Dependent Perturbation Theory and Scattering 8 Semi-Classical and Quantum Electromagnetic Field 9 Emission and Absorption of Radiation 10 Relativistic Quantum Mechanics A Dimensions and Units B Mathematical Tools C Selected Solutions

Quantum Mechanics: An Accessible Introduction (2版)

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【簡介】 This book provides a comprehensive introduction to quantum mechanics from the ground up. It is designed to be completely self-contained and assumes very little knowledge or mathematical background on the part of students as it takes them through the major topics of quantum mechanics. Designed to be appropriate for students across a wide range of abilities and backgrounds, this book will be particularly helpful for students who might lack some of the mathematical background typically assumed in an undergraduate quantum mechanics course. The book includes three "math interludes" covering such topics as complex numbers, linear operators, vector spaces, and matrix manipulation. The book also discusses some interesting modern applications of quantum mechanics: magnetic resonance imaging and quantum computing, and it concludes with an introduction to relativistic quantum theory. This second edition includes expanded and improved coverage of the Heisenberg uncertainty principle, the use of ladder operators to solve the harmonic oscillator, as well as the treatment of the Lamb shift. 【目錄】 The Origins of Quantum Mechanics Math Interlude A: Complex Numbers and Linear Operators The Schrödinger Equation Solutions of the One-Dimensional Time-Independent Schrödinger Equation Math Interlude B: Linear Algebra Solutions of the Three-Dimensional Time-Independent Schrödinger Equation Math Interlude C: Matrices, Dirac Notation, and the Dirac Delta Function Spin Angular Momentum Time-Independent Perturbation Theory The Variational Principle Time-Dependent Perturbation Theory Scattering Theory Multiparticle Schrödinger Equation Modern Applications of Quantum Mechanics Relativistic Quantum Mechanics