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Quantum Mechanics: Introduction to Mathematical Formulation (essentials)
by Martin PieperAnyone who has always wanted to understand the hieroglyphs on Sheldon's blackboard in the television series The Big Bang Theory or who wanted to know exactly what the fate of Schrödinger's cat is all about will find a short, descriptive introduction to the world of quantum mechanics in this essential . In particular, the text focuses on the mathematical description in the Hilbert space. The content goes beyond popular scientific presentations, but is nevertheless suitable for readers without special prior knowledge thanks to the clear examples. This Springer essential is a translation of the original German 1st edition essentials, Quantenmechanik by Martin Pieper published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2019.The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.The author:Prof. Dr. Martin Pieper has been Professor of Mathematics and Simulation at the FH Aachen since 2011. Before he was appointed to the FH Aachen, he was a research assistant in the Optimization department of the Fraunhofer Institute for Industrial Mathematics.
Quantum Mechanics: Inception or Conception? A Classical Preamble to Quantum Mechanics
by Giuseppe PileioEmbarking on a journey into the realm of quantum mechanics can be a daunting task for anyone. Its puzzling mathematics and bewildering predictions often leave individuals feeling confused and disheartened. But what if there was a different approach — one aimed to cultivate an understanding of quantum mechanics from its very foundations? This is the ambition of this book. Rather than treating quantum mechanics as an inception, the author takes a Socratic perspective, tracing the genesis of its key ideas back to the well-established roots of classical mechanics. The works of Lagrange, Hamilton, and Poisson become guiding lights, illuminating the path towards comprehension. Through a colloquial yet pedagogical narrative, the book delves into the elements of classical mechanics, building a solid framework of familiarity that paves the way for comprehending quantum mechanics.Designed as a companion for undergraduates undertaking quantum mechanics modules in physics or chemistry, this book serves as an invaluable support. It equips learners with the essential knowledge necessary to grasp the foundations of quantum mechanics. As such, it proves equally beneficial for MSc and PhD scholars, and post-doctoral researchers. Its colloquial tone captivates the curiosity of any reader eager to delve into the mysteries of this enthralling field.
Quantum Mechanics
by Alastair I. Rae Jim NapolitanoA Thorough Update of One of the Most Highly Regarded Textbooks on Quantum MechanicsContinuing to offer an exceptionally clear, up-to-date treatment of the subject, Quantum Mechanics, Sixth Edition explains the concepts of quantum mechanics for undergraduate students in physics and related disciplines and provides the foundation necessary for other
Quantum Mechanics: An Enhanced Primer
by Bruce Cameron ReedQuantum mechanics is one of the most fascinating elements of the physics curriculum, but its conceptual nuances and mathematical complexity can be daunting for beginning students. This user-friendly text is designed for a one-semester course which bridges the gap between sophomore-level treatments and advanced undergraduate/lower-graduate courses. Qualitative explanations and descriptions of historical background are combined with detailed mathematical analyses to help students establish a firm foundation for further study. Classical problems such potential wells, barrier penetration, alpha decay, the harmonic oscillator, and the hydrogen atom are examined in detail, and formalisms and techniques such as operators, expectation values, commutators, perturbation theory, numerical solutions, and the variational theorem are also covered. Particular emphasis is placed on providing numerous worked examples and exercises.
Quantum Mechanics: A Simplified Approach
by Shabnam SiddiquiQuantum mechanics is one of the most challenging subjects to learn. It is challenging because quantum phenomenon is counterintuitive, and the mathematics used to explain such a phenomenon is very abstract, and difficult to grasp. This textbook is an attempt to overcome these challenges. Every chapter presents quantum ideas step- by- step in a structured way with a comparison between quantum and classical concepts. It provides a clear distinction between classical and quantum logic. Conceptual questions are provided after every important section so that the reader can test their understanding at every step. Such an approach aids in preventing misconceptions. Problem solving is not restricted to solving differential equations and integration. But it requires to systematically and creatively analyze a problem, to apply the new and powerful concepts for finding a solution and to understand the physical meaning of the solution. The tutorials on special topics are an effort to teach problem solving by actively engaging the reader in a thinking process, to apply the concepts and to understand the physical meaning of the solution. The simulations are provided for some of the topics. The simulations aid in the visualization of the quantum phenomenon, and for meaningful understanding of the mathematics. This approach may lead to development of "quantum mechanical intuition "as well as learning mathematical techniques for problem solving. Most importantly, the book is not flooded with numerous topics that makes the reader confused and distracted, rather the most important topics are discussed at a deeper level. The understanding of quantum mechanics is incomplete without understanding the early ideas and experiments that lead to the development of the quantum theory. Thus, the first two chapters of the book are dedicated to such topics. The key features of this book are: A simplified, structured, and step-by-step introduction to quantum mechanics. The simplification is attained through use of two-level system, step- by- step discussion of important topics in a simplified language at a deeper level, analogies, and visualization using illustrations and simulations A systematic arrangement of topics, and numerous worked- out examples. The presentation of the structure in the mathematical formalism of quantum mechanics provides clarity in understanding complicated and abstract mathematics. It also helps to understand the distinction between the quantum mechanical and classical approaches Conceptual questions at the end of every important section. The conceptual questions can be used in a classroom as a point of discussion between an instructor and students Tutorials on special topics. Simulations on special topics aid in the visualization of the physical phenomenon, and demonstration of the application of mathematics An in-depth discussion of the wave-particle duality, measurement problem, and their philosophical implications in Chapter 2 provides an understanding of the broader meaning of quantum mechanics
Quantum Mechanics: The Theoretical Minimum (The Theoretical Minimum)
by Leonard Susskind Art FriedmanFrom the bestselling author of The Theoretical Minimum, an accessible introduction to the math and science of quantum mechanicsQuantum Mechanics is a (second) book for anyone who wants to learn how to think like a physicist. In this follow-up to the bestselling The Theoretical Minimum, physicist Leonard Susskind and data engineer Art Friedman offer a first course in the theory and associated mathematics of the strange world of quantum mechanics. Quantum Mechanics presents Susskind and Friedman's crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics. An accessible but rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.
Quantum Mechanics: Foundations and Applications
by Donald Gary SwansonProgressing from the fundamentals of quantum mechanics (QM) to more complicated topics, Quantum Mechanics: Foundations and Applications provides advanced undergraduate and graduate students with a comprehensive examination of many applications that pertain to modern physics and engineering.Based on courses taught by the author, this textboo
Quantum Mechanics: A Concise Introduction
by Biao WuThis textbook highlights a concise introduction to quantum mechanics in a readable and serious manner. Being readable, the book intends to present the beauty and magic of quantum mechanics to the mass public. Being serious, the book uses mathematics to describe the most profound results in quantum mechanics. To balance the two, the book assumes that the readers are familiar with high-school mathematics and instructs the least possible advanced mathematics necessary for the understanding of quantum mechanics.The book first covers the history of quantum mechanics and then introduces the magical quantum world, including quantum states living in Hilbert space, indistinguishable particles,linear superposition, Heisenberg's uncertainty relations, quantum entanglement, Bell's inequality, quantum energy levels, Schrödinger’s cat and many-worlds theory, etc. To compare with classic physics, the book also covers the classic mechanics before introducing quantum mechanics. At last, the book briefly covers quantum computing and quantum communications. Besides readers of other majors, the book is also a good reference for students in physics. It helps physics students to develop a solid understanding of the basics of quantum mechanics, preventing them from getting lost in solving the Schrödinger equation. The book also discusses quantum entanglement and quantum information which traditional quantum mechanics textbooks do not cover. The Foreword is written by Frank Wilczek, Nobel Laureate in physics, 2004.This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
Quantum Mechanics: Teach Yourself
by Alexandre ZagoskinWritten by Dr Alexandre Zagoskin, who is a Reader at Loughborough University, Quantum Mechanics: A Complete Introduction is designed to give you everything you need to succeed, all in one place. It covers the key areas that students are expected to be confident in, outlining the basics in clear jargon-free English, and then providing added-value features like summaries of key ideas, and even lists of questions you might be asked in your exam. The book uses a structure that is designed to make quantum physics as accessible as possible - by starting with its similarities to Newtonian physics, rather than the rather startling differences.
Quantum Mechanics and Avant-Garde Music: Shadows of the Void
by Rakhat-Bi Abdyssagin"Fascinating details and anecdotes accompany this engaging account of the emergence of dramatic new ideas and forms in music over the centuries..." David Politzer, winner of the 2004 Nobel Prize in Physics. "A thought-provoking, stimulating, and highly original exploration of deep metaphorical links between music and physics...Highly recommended." Prof. Ian Stewart FRS, author, What’s the Use? "An astonishing book!" Tristan Murail, composer and co-creator of the "spectral" technique. Have you ever wondered about the connection between Pauli's exclusion principle and Schoenberg's dodecaphony? Or the symphonic echoes of Heisenberg's uncertainty principle in the compositions of Stockhausen and Cage? This book not only poses these questions but skillfully uncovers the artistic answers, exploring interdisciplinary connections that bridge the gap between modern physics and contemporary music. Dive into philosophical discourses on time, witness the metamorphosis of Boolean algebra, bits, and qubits into musical notation, and discover the limitations of the 12-tone scale mirrored in the speed of light. The author's unique methodology offers a fresh perspective, linking the language of mathematics and physics to the creation of musical scores. This book transcends the boundaries of physics and music, revealing the inevitable fusion of modern physics and avant-garde music in the twentieth century. Through meticulous research, the author showcases the profound impact of revolutionary ideas such as quantum physics and relativity on all aspects of life and demonstrates that modern physics and contemporary music were born not out of chance—their emergence and development were inevitable events. Delving into the historical accounts, he explores the musical endeavors of great physicists like Max Planck and Albert Einstein, unraveling the quantum entanglement of physics mirrored in the extended techniques of contemporary music and unveiling the musical universe of Werner Heisenberg through captivating personal encounters with his descendants. Crafted for general readers and seasoned experts alike, the book maintains clarity and style, ensuring accessibility without sacrificing depth. This pioneering exploration not only draws connections between modern physics and music but also serves as a unique bridge for scientists, musicians, and the curious general audience. Requiring no formal background in physics or music, the book is a compelling read for those intrigued by the uncharted territories where science and art converge, offering a concise and illuminating journey into the shadows of the void.
Quantum Mechanics and Experience
by David Z. AlbertThe more science tells us about the world, the stranger it looks. Ever since physics first penetrated the atom, early in this century, what it found there has stood as a radical and unanswered challenge to many of our most cherished conceptions of nature. It has literally been called into question since then whether or not there are always objective matters of fact about the whereabouts of subatomic particles, or about the locations of tables and chairs, or even about the very contents of our thoughts. A new kind of uncertainty has become a principle of science. This book is an original and provocative investigation of that challenge, as well as a novel attempt at writing about science in a style that is simultaneously elementary and deep. It is a lucid and self-contained introduction to the foundations of quantum mechanics, accessible to anyone with a high school mathematics education, and at the same time a rigorous discussion of the most important recent advances in our understanding of that subject, some of which are due to the author himself.
Quantum Mechanics and Fundamentality: Naturalizing Quantum Theory between Scientific Realism and Ontological Indeterminacy (Synthese Library #460)
by Valia AlloriThis edited collection provides new perspectives on some metaphysical questions arising in quantum mechanics. These questions have been long-standing and are of continued interest to researchers and graduate students working in physics, philosophy of physics, and metaphysics. It features contributions from a diverse set of researchers, ranging from senior scholars to junior academics, working in varied fields, from physics to philosophy of physics and metaphysics. The contributors reflect on issues about fundamentality (is quantum theory fundamental? If so, what is its fundamental ontology?), ontological dependence (how do ordinary objects exist even if they are not fundamental?), realism (what kind of realism is compatible with quantum theory?), indeterminacy (can the world itself exhibit ontological indeterminacy?). The book contains contributions from both physicists (including Nobel Prize winner Gerard 't Hooft), science communicators and philosophers.
Quantum Mechanics and Quantum Field Theory
by Jonathan DimockExplaining the concepts of quantum mechanics and quantum field theory in a precise mathematical language, this textbook is an ideal introduction for graduate students in mathematics, helping to prepare them for further studies in quantum physics. The textbook covers topics that are central to quantum physics: non-relativistic quantum mechanics, quantum statistical mechanics, relativistic quantum mechanics and quantum field theory. There is also background material on analysis, classical mechanics, relativity and probability. Each topic is explored through a statement of basic principles followed by simple examples. Around 100 problems throughout the textbook help readers develop their understanding.
Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints (SpringerBriefs in Physics)
by Albert SchwarzThis book offers a non-standard introduction to quantum mechanics and quantum field theory, approaching these topics from algebraic and geometric perspectives. Beginning with fundamental notions of quantum theory and the derivation of quantum probabilities from decoherence, it proceeds to prove the expression for the scattering matrix in terms of Green functions (LSZ formula), along with a similar expression for the inclusive scattering matrix. The exposition relies on recent findings by the author that provide a deeper understanding of the structure of quantum theory and extend beyond its traditional boundaries. The book is suitable for graduate students and young researchers in mathematics and theoretical physics seeking to delve into innovative concepts within quantum theory. The book contains many recent results therefore it should be interesting also to accomplished physicists and mathematicians.
Quantum Mechanics and Quantum Information
by Vadim Fayngold Moses FayngoldA thorough definition of the basic concepts of quantum mechanics and quantum information and their interrelations. Alongside a thorough definition of the basic concepts and their interrelations, backed by numerous examples, this textbook features a rare discussion of the quantum information theory. It also deals with other important topics hardly found in the literature, including the Robertson-Schrodinger-relation, angle and angular momentum uncertainties, interaction-free measurements, and the limitations of the no-cloning theorem.With its interpretations of quantum mechanics and its discussions of quantum computing, this book is poised to become the standard textbook for advanced undergraduate and beginning graduate quantum mechanics courses and as an essential reference for physics students and physics professionals.
Quantum Mechanics and the Philosophy of Alfred North Whitehead: And the Philosophy of Alfred North Whitehead (American Philosophy)
by Michael EppersonIn Process and Reality and other works, Alfred North Whitehead struggled to come to terms with the impact the new science of quantum mechanics would have on metaphysics.This ambitious book is the first extended analysis of the intricate relationships between relativity theory, quantum mechanics, and Whitehead's cosmology. Michael Epperson illuminates the intersection of science and philosophy in Whitehead's work-and details Whitehead's attempts to fashion an ontology coherent with quantum anomalies.Including a nonspecialist introduction to quantum mechanics, Epperson adds an essential new dimension to our understanding of Whitehead-and of the constantly enriching encounter between science and philosophy in our century.
Quantum Mechanics Between Ontology and Epistemology (European Studies in Philosophy of Science #10)
by Florian J. BogeThis book explores the prospects of rivaling ontological and epistemic interpretations of quantum mechanics (QM). It concludes with a suggestion for how to interpret QM from an epistemological point of view and with a Kantian touch. It thus refines, extends, and combines existing approaches in a similar direction. The author first looks at current, hotly debated ontological interpretations. These include hidden variables-approaches, Bohmian mechanics, collapse interpretations, and the many worlds interpretation. He demonstrates why none of these ontological interpretations can claim to be the clear winner amongst its rivals. Next, coverage explores the possibility of interpreting QM in terms of knowledge but without the assumption of hidden variables. It examines QBism as well as Healey’s pragmatist view. The author finds both interpretations or programs appealing, but still wanting in certain respects. As a result, he then goes on to advance a genuine proposal as to how to interpret QM from the perspective of an internal realism in the sense of Putnam and Kant. The book also includes two philosophical interludes. One details the notions of probability and realism. The other highlights the connections between the notions of locality, causality, and reality in the context of violations of Bell-type inequalities.
Quantum Mechanics: A Complete Introduction: Teach Yourself
by Alexandre ZagoskinWritten by Dr Alexandre Zagoskin, who is a Reader at Loughborough University, Quantum Mechanics: A Complete Introduction is designed to give you everything you need to succeed, all in one place. It covers the key areas that students are expected to be confident in, outlining the basics in clear jargon-free English, and then providing added-value features like summaries of key ideas, and even lists of questions you might be asked in your exam. The book uses a structure that is designed to make quantum physics as accessible as possible - by starting with its similarities to Newtonian physics, rather than the rather startling differences.
The Quantum Mechanics Conundrum: Interpretation and Foundations
by Gennaro AulettaThis comprehensive volume gives a balanced and systematic treatment of both the interpretation and the mathematical-conceptual foundations of quantum mechanics. It is written in a pedagogical style and addresses many thorny problems of fundamental physics.The first aspect concerns Interpretation. The author raises the central problems: formalism, measurement, non-locality, and causality. The main positions on these subjects are presented and critically analysed. The aim is to show that the main schools can converge on a core interpretation. The second aspect concerns Foundations. Here it is shown that the whole theory can be grounded on information theory. The distinction between information and signal leads us to integrating quantum mechanics and relativity. Category theory is presented and its significance for quantum information shown; the logic and epistemological bases of the theory are assessed.Of relevance to all physicists and philosophers with an interest in quantum theory and its foundations, this book is destined to become a classic work.
Quantum Mechanics for Applied Physics and Engineering
by Albert T. Fromhold Jr.For upper-level undergraduates and graduate students: an introduction to the fundamentals of quantum mechanics, emphasizing aspects essential to an understanding of solid-state theory. A heavy background in mathematics and physics is not required beyond basic courses in calculus, differential equations, and calculus-based elementary physics. Numerous problems (and selected answers), projects, exercises.
Quantum Mechanics for Chemistry
by Seogjoo J. JangThis textbook forms the basis for an advanced undergraduate or graduate level quantum chemistry course, and can also serve as a reference for researchers in physical chemistry and chemical physics. In addition to the standard core topics such as principles of quantum mechanics, vibrational and rotational states, hydrogen-like molecules, perturbation theory, variational principles, and molecular orbital theories, this book also covers essential theories of electronic structure calculation, the primary methods for calculating quantum dynamics, and major spectroscopic techniques for quantum measurement. Plus, topics that are overlooked in conventional textbooks such as path integral formulation, open system quantum dynamics methods, and Green’s function approaches are addressed. This book helps readers grasp the essential quantum mechanical principles and results that serve as the foundation of modern chemistry and become knowledgeable in major methods of computational chemistry and spectroscopic experiments being conducted by present-day researchers. Dirac notation is used throughout, and right balance between comprehensiveness, rigor, and readability is achieved, ensuring that the book remains accessible while providing all the relevant details. Complete with exercises, this book is ideal for a course on quantum chemistry or as a self-study resource.
Quantum Mechanics for Material Science: An Introduction
by Gianluca StefanucciThis book is based on the course "Elements of Theoretical Physics," which the author has been teaching at the University of Rome Tor Vergata since 2017. It serves as an introduction to quantum mechanics, providing students with essential concepts and tools for future lessons, while still maintaining a comprehensive approach without relying heavily on the level of abstraction and mathematical rigor typically found in Physics programs. Understanding this book only requires knowledge of the mathematical concepts taught in the first two years of basic courses. The bachelor's degree program in Materials Science aims to train students with an interdisciplinary background in physics, chemistry, and engineering. While the study of quantum mechanics is essential, the same level of depth, abstraction, and mathematical rigor as in a Physics degree program is not a requirement. Unfortunately, most textbooks on Quantum Mechanics are geared toward Physics students, making it difficult to find suitable resources for Materials Science students. To make learning easier, the author has chosen not to refer students to various textbooks for different topics. Instead, he has created handouts that have evolved into a condensed textbook on quantum mechanics specifically tailored to the needs of the Materials Science program.
Quantum Mechanics for Pedestrians 1: Fundamentals
by Jochen PadeThis book provides an introduction into the fundamentals of non-relativistic quantum mechanics. In Part 1, the essential principles are developed. Applications and extensions of the formalism can be found in Part 2. The book includes not only material that is presented in traditional textbooks on quantum mechanics, but also discusses in detail current issues such as interaction-free quantum measurements, neutrino oscillations, various topics in the field of quantum information as well as fundamental problems and epistemological questions, such as the measurement problem, entanglement, Bell's inequality, decoherence, and the realism debate. A chapter on current interpretations of quantum mechanics concludes the book. To develop quickly and clearly the main principles of quantum mechanics and its mathematical formulation, there is a systematic change between wave mechanics and algebraic representation in the first chapters. The required mathematical tools are introduced step by step. Moreover, the appendix collects compactly the most important mathematical tools that supplementary literature can be largely dispensed. In addition, the appendix contains advanced topics, such as Quantum- Zeno effect, time-delay experiments, Lenz vector and the Shor algorithm. About 250 exercises, most of them with solutions, help to deepen the understanding of the topics. Target groups of the book are student teachers and all students of physics, as minor or major, looking for a reasonably easy and modern introduction into quantum mechanics.
Quantum Mechanics for Pedestrians 1: Fundamentals (Undergraduate Lecture Notes in Physics)
by Jochen PadeThis book, the first in a two-volume set, provides an introduction to the fundamentals of (mainly) non-relativistic quantum mechanics. This first volume chiefly focuses on the essential principles, while applications and extensions of the formalism can be found in volume 2. Including but also moving beyond material that is covered in traditional textbooks on quantum mechanics, the book discusses in detail current issues such as interaction-free quantum measurements or neutrino oscillations, as well as fundamental problems and epistemological questions, such as the measurement problem. A chapter on the postulates of quantum mechanics rounds off this first volume. In order to quickly and clearly present the main principles of quantum mechanics and its mathematical formulation, there is a systematic transition between wave mechanics and algebraic representation in the first few chapters, in which the required mathematical tools are introduced step by step. Moreover, the appendix concisely reviews the most important mathematical tools, allowing readers to largely dispense with supplementary literature. The appendix also explores advanced topics, such as the Quantum-Zeno effect and time-delay experiments. Over 250 exercises, most of them with solutions, help to deepen the reader’s understanding of the topics discussed. This revised second edition is expanded by an introduction to some ideas and problems of relativistic quantum mechanics. In this first volume, the Klein-Gordon and the Dirac equations are treated. Fundamentals of other areas are compiled in compact form, i.e., outlines of special relativity, classical field theory and electrodynamics. The book is chiefly intended for student science teachers and all students of physics, majors and minors alike, who are looking for a reasonably easy and modern introduction to quantum mechanics.
Quantum Mechanics for Pedestrians 2: Applications and Extensions
by Jochen PadeThe two-volume textbook Quantum Mechanics for Pedestrians provides an introduction to the basics of nonrelativistic quantum mechanics. Originally written as a course for students of science education, the book addresses all those science students and others who are looking for a reasonably simple, fresh and modern introduction to the field. The basic principles of quantum mechanics are presented in the first volume. This second volume discusses applications and extensions to more complex problems. In addition to topics traditionally dealt with in quantum mechanics texts, such as symmetries or many-body problems, here also issues of current interest such as entanglement, Bell's inequalities, decoherence and various aspects of quantum information are treated in detail. Furthermore, questions of the basis of quantum mechanics and epistemological issues are discussed explicitly; these are relevant e. g. to the realism debate. A chapter on the interpretations of quantum mechanics completes this volume. The necessary mathematical tools are introduced step by step; in the appendix, the most relevant mathematics is compiled in compact form. More advanced topics such as the Lenz vector, Hardy's experiment and Shor's algorithm are treated in more detail in the appendix. As an essential aid to learning and teaching, 130 exercises are included, most of them with their solutions.