A Mathematical Journey To Quantum Mechanics
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A Mathematical Journey To Quantum Mechanics
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Author : Salvatore Capozziello
language : en
Publisher: Springer Nature
Release Date : 2021-09-27
A Mathematical Journey To Quantum Mechanics written by Salvatore Capozziello and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-27 with Science categories.
This book provides an itinerary to quantum mechanics taking into account the basic mathematics to formulate it. Specifically, it features the main experiments and postulates of quantum mechanics pointing out their mathematical prominent aspects showing how physical concepts and mathematical tools are deeply intertwined. The material covers topics such as analytic mechanics in Newtonian, Lagrangian, and Hamiltonian formulations, theory of light as formulated in special relativity, and then why quantum mechanics is necessary to explain experiments like the double-split, atomic spectra, and photoelectric effect. The Schrödinger equation and its solutions are developed in detail. It is pointed out that, starting from the concept of the harmonic oscillator, it is possible to develop advanced quantum mechanics. Furthermore, the mathematics behind the Heisenberg uncertainty principle is constructed towards advanced quantum mechanical principles. Relativistic quantum mechanics is finally considered.The book is devoted to undergraduate students from University courses of Physics, Mathematics, Chemistry, and Engineering. It consists of 50 self-contained lectures, and any statement and theorem are demonstrated in detail. It is the companion book of "A Mathematical Journey to Relativity", by the same Authors, published by Springer in 2020.
A Mathematical Journey Through Differential Equations Of Physics
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Author : Max Lein
language : en
Publisher: World Scientific
Release Date : 2022-09-16
A Mathematical Journey Through Differential Equations Of Physics written by Max Lein and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-16 with Science categories.
Mathematics is the language of physics, and over time physicists have developed their own dialect. The main purpose of this book is to bridge this language barrier, and introduce the readers to the beauty of mathematical physics. It shows how to combine the strengths of both approaches: physicists often arrive at interesting conjectures based on good intuition, which can serve as the starting point of interesting mathematics. Conversely, mathematicians can more easily see commonalities between very different fields (such as quantum mechanics and electromagnetism), and employ more advanced tools.Rather than focusing on a particular topic, the book showcases conceptual and mathematical commonalities across different physical theories. It translates physical problems to concrete mathematical questions, shows how to answer them and explains how to interpret the answers physically. For example, if two Hamiltonians are close, why are their dynamics similar?The book alternates between mathematics- and physics-centric chapters, and includes plenty of concrete examples from physics as well as 76 exercises with solutions. It exploits that readers from either end are familiar with some of the material already. The mathematics-centric chapters provide the necessary background to make physical concepts mathematically precise and establish basic facts. And each physics-centric chapter introduces physical theories in a way that is more friendly to mathematicians.As the book progresses, advanced material is sprinkled in to showcase how mathematics and physics augment one another. Some of these examples are based on recent publications and include material which has not been covered in other textbooks. This is to keep it interesting for the readers.
A Mathematical Journey
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-03-17
A Mathematical Journey written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-17 with Mathematics categories.
Embark on an intellectual journey into the realm of logic, where reasoning and argumentation unveil the secrets of truth and validity. Discover the foundations of logic, unraveling the intricacies of propositions, truth values, and logical connectives. Explore the power of deductive and inductive reasoning, crafting sound arguments and evaluating their validity. Witness the practical applications of logic in various fields, from philosophy and mathematics to law and everyday life. Delve into the fascinating world of propositional logic and predicate logic, uncovering the mechanisms that govern the validity of logical statements. Explore the intricacies of truth tables, logical equivalence, and the laws of logic, appreciating the elegance and rigor of logical reasoning. Investigate the realm of set theory and functions, encountering fundamental concepts like sets, elements, and set operations. Discover the properties of functions and relations, witnessing their patterns and underlying structures. Witness the practical applications of these concepts in diverse disciplines, from computer science and mathematics to economics and social sciences. Venture into the frontiers of mathematical logic, where Gödel's incompleteness theorems challenge our understanding of truth, provability, and the foundations of mathematics itself. Explore the intricate world of recursive functions and the halting problem, contemplating the limits of computability and the boundaries of human knowledge. Encounter the vibrant world of non-classical logics, where fuzzy logic, modal logic, and intuitionistic logic offer alternative perspectives on truth, possibility, and necessity. Expand your understanding of the diverse ways in which we can reason and draw conclusions. Throughout this captivating exploration, you will uncover the beauty, power, and far-reaching applications of logic. With each chapter, you will gain a profound understanding of logical reasoning, its role in shaping our world, and its ability to expand the boundaries of human knowledge. This book is an indispensable resource for students, researchers, and anyone seeking to master the art of logical reasoning and unlock the secrets of truth and validity. If you like this book, write a review!
Mathematical Concepts Of Quantum Mechanics
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Author : Stephen J. Gustafson
language : en
Publisher: Springer Nature
Release Date : 2020-10-21
Mathematical Concepts Of Quantum Mechanics written by Stephen J. Gustafson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-21 with Mathematics categories.
The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with 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 more advanced topics presented include: many-body systems, modern perturbation theory, path integrals, the theory of resonances, adiabatic theory, geometrical phases, Aharonov-Bohm effect, density functional theory, open systems, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. Some of the sections could be used for introductions to geometrical methods in Quantum Mechanics, to quantum information theory and to quantum electrodynamics and quantum field theory.
A Mathematical Journey To Relativity
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Author : Wladimir-Georges Boskoff
language : en
Publisher: Springer Nature
Release Date : 2020-06-01
A Mathematical Journey To Relativity written by Wladimir-Georges Boskoff and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-01 with Science categories.
This book opens with an axiomatic description of Euclidean and non-Euclidean geometries. Euclidean geometry is the starting point to understand all other geometries and it is the cornerstone for our basic intuition of vector spaces. The generalization to non-Euclidean geometry is the following step to develop the language of Special and General Relativity. These theories are discussed starting from a full geometric point of view. Differential geometry is presented in the simplest way and it is applied to describe the physical world. The final result of this construction is deriving the Einstein field equations for gravitation and spacetime dynamics. Possible solutions, and their physical implications are also discussed: the Schwarzschild metric, the relativistic trajectory of planets, the deflection of light, the black holes, the cosmological solutions like de Sitter, Friedmann-Lemaître-Robertson-Walker, and Gödel ones. Some current problems like dark energy are also scketched. The book is self-contained and includes details of all proofs. It provides solutions or tips to solve problems and exercises. It is designed for undergraduate students and for all readers who want a first geometric approach to Special and General Relativity.
Hilbert S Voyage A Journey Through The World Of Infinite Dimensions
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-03-17
Hilbert S Voyage A Journey Through The World Of Infinite Dimensions written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-17 with Mathematics categories.
Embark on a captivating journey through the realm of infinite dimensions with "Hilbert's Voyage: A Journey Through the World of Infinite Dimensions." This comprehensive guide unveils the profound applications of Hilbert spaces in diverse fields, ranging from quantum mechanics and signal processing to approximation theory and numerical analysis. Discover the elegance and power of Hilbert spaces, mathematical structures that extend the concepts of Euclidean geometry to infinite dimensions. These spaces provide a framework for understanding complex phenomena, from the behavior of subatomic particles to the analysis of signals and images. Delve into the fundamental concepts of Hilbert spaces, including inner products, orthogonality, and completeness. Uncover their applications in quantum mechanics, where they provide a mathematical foundation for describing the behavior of quantum systems. Explore the beauty of orthogonality and its significance in signal processing and data analysis, enabling the extraction of meaningful information from complex datasets. Investigate the role of operators on Hilbert spaces, which represent physical quantities and transformations. Discover their profound implications in quantum mechanics, where they govern the evolution of quantum states. Witness the interplay between Hilbert spaces and functional analysis, leading to powerful abstract tools for solving complex problems. Journey into the realm of Hilbert spaces in mathematical physics, where they provide a framework for understanding quantum mechanics, statistical mechanics, and quantum field theory. Explore their applications in signal processing and communication theory, where they facilitate the analysis and manipulation of signals. Delve into approximation theory, where Hilbert spaces enable the approximation of functions and curves with remarkable accuracy. Navigate the frontiers of numerical analysis, where Hilbert spaces play a pivotal role in solving partial differential equations and simulating complex phenomena. Conclude your voyage with a glimpse into the future of Hilbert space theory, highlighting open questions and potential new directions for research. "Hilbert's Voyage" is a captivating exploration of Hilbert spaces, their applications, and their profound impact on science, technology, and our understanding of the universe. It is an essential resource for mathematicians, physicists, engineers, and anyone seeking to deepen their understanding of this fascinating mathematical concept. If you like this book, write a review!
Number Theory In Quantum Mechanics
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Author : N.B. Singh
language : en
Publisher: N.B. Singh
Release Date :
Number Theory In Quantum Mechanics written by N.B. Singh and has been published by N.B. Singh this book supported file pdf, txt, epub, kindle and other format this book has been release on with Science categories.
"Number Theory in Quantum Mechanics" is a specialized exploration that bridges the realms of number theory and quantum mechanics. Catering to students, physicists, and researchers in quantum physics, this book investigates the intriguing connections between number theory concepts and quantum phenomena. Covering topics such as quantum states, operators, and wave functions, the book illuminates the mathematical underpinnings that emerge when applying number theory principles to quantum mechanics. With clarity and depth, this book serves as a valuable resource for those intrigued by the intersection of mathematical theory and quantum physics, offering new perspectives on the fundamental nature of quantum systems.
A Mathematician S Journeys
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Author : Alexander Jones
language : en
Publisher: Springer
Release Date : 2016-02-03
A Mathematician S Journeys written by Alexander Jones and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-03 with History categories.
This book explores facets of Otto Neugebauer's career, his impact on the history and practice of mathematics, and the ways in which his legacy has been preserved or transformed in recent decades, looking ahead to the directions in which the study of the history of science will head in the twenty-first century. Neugebauer, more than any other scholar of recent times, shaped the way we perceive premodern science. Through his scholarship and influence on students and collaborators, he inculcated both an approach to historical research on ancient and medieval mathematics and astronomy through precise mathematical and philological study of texts, and a vision of these sciences as systems of knowledge and method that spread outward from the ancient Near Eastern civilizations, crossing cultural boundaries and circulating over a tremendous geographical expanse of the Old World from the Atlantic to India.
Mathematical Results In Quantum Mechanics Proceedings Of The Qmath12 Conference With Dvd Rom
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Author : Pavel Exner
language : en
Publisher: World Scientific
Release Date : 2014-11-13
Mathematical Results In Quantum Mechanics Proceedings Of The Qmath12 Conference With Dvd Rom written by Pavel Exner and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-13 with Mathematics categories.
The book provides a comprehensive overview on the state of the art of the quantum part of mathematical physics. In particular, it contains contributions to the spectral theory of Schrödinger and random operators, quantum field theory, relativistic quantum mechanics and interacting many-body systems.It also presents an overview on the achievements in mathematical physics since the last conference QMath11 held at Hradec Kralove, Czechia in 2010.
Untangling Space Time Conundrums A Journey Through Twisted Geometries
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-03-15
Untangling Space Time Conundrums A Journey Through Twisted Geometries written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-15 with Science categories.
Journey into the enigmatic realm of spacetime with "Untangling Space-Time Conundrums: A Journey Through Twisted Geometries," a captivating exploration of twistorial geometry, where mathematics and physics intertwine to unveil the hidden wonders of the cosmos. Within these pages, embark on an intellectual odyssey that delves into the profound concepts of spinors, twistors, and conformal geometry, revealing their significance in unraveling the mysteries of space, time, and gravity. Discover how twistors provide a unique lens through which to explore the intricate tapestry of spacetime, offering insights into the nature of black holes, quantum gravity, and the fundamental symmetries of the universe. Prepare to be captivated by the elegance and power of mathematical tools such as knot theory, which unveils the hidden knots and tangles that permeate the fabric of spacetime. Witness the interplay of abstract concepts and physical phenomena as we unravel the secrets of null geodesics, the paths of light that illuminate the universe. This book is an invitation to embark on a journey beyond the boundaries of conventional understanding, to explore the frontiers of human knowledge and question the very nature of reality. With each chapter, you will delve deeper into the intricacies of twistorial geometry, gaining a profound appreciation for the harmonious interplay of mathematics and physics. "Untangling Space-Time Conundrums" is a masterpiece that will challenge your intellect, ignite your curiosity, and leave you in awe of the universe's hidden wonders. Join us on this extraordinary voyage through twisted geometries, where the mysteries of spacetime unravel before your very eyes. If you like this book, write a review!