Mathematical Concepts Of Quantum Mechanics

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Mathematical Concepts Of Quantum Mechanics

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Author : Stephen J. Gustafson
language : en
Publisher: Springer Science & Business Media
Release Date : 2003

Mathematical Concepts Of Quantum Mechanics written by Stephen J. Gustafson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Education categories.

The book gives a streamlined introduction to quantum mechanics, while describing the basic mathematical structures underpinning this discipline. Starting with an overview of the key physical experiments illustrating the origin of the physical foundations, the book proceeds to a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The topics presented include spectral theory, many-body theory, positive temperatures, path integrals and quasiclassical asymptotics, the theory of resonances, an introduction to quantum field theory and the theory of radiation. The book can serve as a text for an intermediate course in quantum mechanics, or a more advanced topics course.

Mathematical Concepts Of Quantum Mechanics

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Author : Stephen J Gustafson
language : en
Publisher:
Release Date : 2003-07-28

Mathematical Concepts Of Quantum Mechanics written by Stephen J Gustafson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-28 with categories.

Quantum Mechanics

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Author : Leslie E. Ballentine
language : en
Publisher: World Scientific
Release Date : 1998

Quantum Mechanics written by Leslie E. Ballentine and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Science categories.

"the book is of greatest benefit to students of quantum mechanics who want to learn more than solely computational recipes and predictive tools of the theory, and, in this sense, the book really fills a gap in the literature".Mathematical Reviews, 1999

Mathematical Universe Concepts

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Author : Eleanor Hawking
language : en
Publisher: Publifye AS
Release Date : 2025-01-06

Mathematical Universe Concepts written by Eleanor Hawking and has been published by Publifye AS this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-06 with Philosophy categories.

""Mathematical Universe Concepts"" explores the profound relationship between mathematics and physical reality, investigating whether mathematical structures are discovered or invented. This thought-provoking work examines how abstract mathematical principles manifest in our observable universe, challenging traditional boundaries between pure mathematics and physical phenomena. Through careful examination of symmetry principles, quantum theory, and complex systems, the book builds a compelling case for mathematics as a fundamental component of reality rather than just a descriptive tool. The book progresses methodically through three major sections, beginning with the mathematical foundations of space, time, and matter. Drawing from both classical and quantum physics, it demonstrates how symmetry principles govern fundamental forces and particle behavior, before culminating in an exploration of complex systems emergence. Real-world evidence from particle accelerator experiments, cosmological observations, and computer simulations supports the theoretical framework, making abstract concepts tangible for readers with basic calculus knowledge. What sets this book apart is its interdisciplinary approach, connecting mathematical physics to fields like evolutionary biology and cognitive science. By presenting complex ideas through carefully chosen analogies and visual representations, it makes advanced theoretical concepts accessible to educated general readers while maintaining scientific rigor. The work serves as an invaluable bridge between pure mathematics and physical sciences, offering fresh perspectives on fundamental questions about the nature of reality and the mathematical underpinnings of our universe.

Quantum Theory For Math Enthusiasts

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Author : Sanjay Nair
language : en
Publisher: Educohack Press
Release Date : 2025-02-20

Quantum Theory For Math Enthusiasts written by Sanjay Nair and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.

"Quantum Theory for Math Enthusiasts" is tailored for undergraduate students with a strong mathematical background who wish to explore the profound connections between mathematics and quantum mechanics. We offer a comprehensive yet accessible introduction to the mathematical foundations of quantum mechanics. Starting with fundamental concepts from linear algebra, functional analysis, and probability theory, we gradually build the mathematical toolkit necessary to understand quantum theory. Through clear explanations, illustrative examples, and exercises, students will develop a solid understanding of Hilbert spaces, operators, eigenvalues, and other key mathematical structures underpinning quantum mechanics. We also explore advanced topics such as symmetry groups, Lie algebras, and representation theory, shedding light on the profound mathematical structures inherent in quantum theory. Whether you're a mathematics major interested in theoretical physics or a physics student looking to deepen your mathematical understanding, our book provides the foundation to appreciate the beauty and elegance of quantum theory from a mathematical perspective.

Understanding Mathematical Concepts In Physics

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Author : Sanjeev Dhurandhar
language : en
Publisher: Springer Nature
Release Date : 2024-07-16

Understanding Mathematical Concepts In Physics written by Sanjeev Dhurandhar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-16 with Science categories.

Modern mathematics has become an essential part of today’s physicist’s arsenal and this book covers several relevant such topics. The primary aim of this book is to present key mathematical concepts in an intuitive way with the help of geometrical and numerical methods - understanding is the key. Not all differential equations can be solved with standard techniques. Examples illustrate how geometrical insights and numerical methods are useful in understanding differential equations in general but are indispensable when extracting relevant information from equations that do not yield to standard methods. Adopting a numerical approach to complex analysis it is shown that Cauchy’s theorem, the Cauchy integral formula, the residue theorem, etc. can be verified by performing hands-on computations with Python codes. Figures elucidate the concept of poles and essential singularities. Further the book covers topology, Hilbert spaces, Fourier transforms (discussing how fast Fourier transform works), modern differential geometry, Lie groups and Lie algebras, probability and useful probability distributions, and statistical detection of signals. Novel features include: (i) Topology is introduced via the notion of continuity on the real line which then naturally leads to topological spaces. (ii) Data analysis in a differential geometric framework and a general description of χ2 discriminators in terms of vector bundles. This book is targeted at physics graduate students and at theoretical (and possibly experimental) physicists. Apart from research students, this book is also useful to active physicists in their research and teaching.

The Theory Of Groups And Quantum Mechanics

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Author : Hermann Weyl
language : en
Publisher: Courier Corporation
Release Date : 1950-01-01

The Theory Of Groups And Quantum Mechanics written by Hermann Weyl and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1950-01-01 with Mathematics categories.

This landmark among mathematics texts applies group theory to quantum mechanics, first covering unitary geometry, quantum theory, groups and their representations, then applications themselves — rotation, Lorentz, permutation groups, symmetric permutation groups, and the algebra of symmetric transformations.

What Is A Mathematical Concept

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Author : Elizabeth de Freitas
language : en
Publisher: Cambridge University Press
Release Date : 2017-06-22

What Is A Mathematical Concept written by Elizabeth de Freitas and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-22 with Education categories.

Leading thinkers in mathematics, philosophy and education offer new insights into the fundamental question: what is a mathematical concept?

Fundamental Mathematical Concepts For Machine Learning In Science

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Author : Umberto Michelucci
language : en
Publisher: Springer Nature
Release Date : 2024-05-16

Fundamental Mathematical Concepts For Machine Learning In Science written by Umberto Michelucci and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-16 with Mathematics categories.

This book is for individuals with a scientific background who aspire to apply machine learning within various natural science disciplines—such as physics, chemistry, biology, medicine, psychology and many more. It elucidates core mathematical concepts in an accessible and straightforward manner, maintaining rigorous mathematical integrity. For readers more versed in mathematics, the book includes advanced sections that are not prerequisites for the initial reading. It ensures concepts are clearly defined and theorems are proven where it's pertinent. Machine learning transcends the mere implementation and training of algorithms; it encompasses the broader challenges of constructing robust datasets, model validation, addressing imbalanced datasets, and fine-tuning hyperparameters. These topics are thoroughly examined within the text, along with the theoretical foundations underlying these methods. Rather than concentrating on particular algorithms this book focuses on the comprehensive concepts and theories essential for their application. It stands as an indispensable resource for any scientist keen on integrating machine learning effectively into their research. Numerous texts delve into the technical execution of machine learning algorithms, often overlooking the foundational concepts vital for fully grasping these methods. This leads to a gap in using these algorithms effectively across diverse disciplines. For instance, a firm grasp of calculus is imperative to comprehend the training processes of algorithms and neural networks, while linear algebra is essential for the application and efficient training of various algorithms, including neural networks. Absent a solid mathematical base, machine learning applications may be, at best, cursory, or at worst, fundamentally flawed. This book lays the foundation for a comprehensive understanding of machine learning algorithms and approaches.

The Mathematical Representation Of Physical Reality

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Author : Shahen Hacyan
language : en
Publisher: Springer Nature
Release Date : 2023-03-06

The Mathematical Representation Of Physical Reality written by Shahen Hacyan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-06 with Science categories.

​This book deals with the rise of mathematics in physical sciences, beginning with Galileo and Newton and extending to the present day. The book is divided into two parts. The first part gives a brief history of how mathematics was introduced into physics—despite its "unreasonable effectiveness" as famously pointed out by a distinguished physicist—and the criticisms it received from earlier thinkers. The second part takes a more philosophical approach and is intended to shed some light on that mysterious effectiveness. For this purpose, the author reviews the debate between classical philosophers on the existence of innate ideas that allow us to understand the world and also the philosophically based arguments for and against the use of mathematics in physical sciences. In this context, Schopenhauer’s conceptions of causality and matter are very pertinent, and their validity is revisited in light of modern physics. The final question addressed is whether the effectiveness of mathematics can be explained by its “existence” in an independent platonic realm, as Gödel believed. The book aims at readers interested in the history and philosophy of physics. It is accessible to those with only a very basic (not professional) knowledge of physics.