UNITEXT for Physics – serie

This textbook is a unique and ambitious primer of nuclear physics, which introduces recent theoretical and experimental progresses starting from basics in fundamental quantum mechanics. The highlight is to offer an overview of nuclear structure phenomena relevant to recent key findings such as unstable halo nuclei, superheavy elements, neutron stars, nucleosynthesis, the standard model, lattice quantum chromodynamics (LQCD), and chiral effective theory. An additional attraction is that general properties of nuclei are comprehensively explained from both the theoretical and experimental viewpoints. The book begins with the conceptual and mathematical basics of quantum mechanics, and goes into the main point of nuclear physics – nuclear structure, radioactive ion beam physics, and nuclear reactions. The last chapters devote interdisciplinary topics in association with astrophysics and particle physics. A number of illustrations and exercises with complete solutions are given. Each chapter is comprehensively written starting from fundamentals to gradually reach modern aspects of nuclear physics with the objective to provide an effective description of the cutting edge in the field.

This book addresses the theoretical foundations and the main physical consequences of electromagnetic interaction, generally considered to be one of the four fundamental interactions in nature, in a mathematically rigorous yet straightforward way. The major focus is on the unifying features shared by classical electrodynamics and all other fundamental relativistic classical field theories. The book presents a balanced blend of derivations of phenomenological predictions from first principles on the one hand, and concrete applications on the other. Further, it highlights the internal inconsistencies of classical electrodynamics, and addresses and resolves often-ignored critical issues, such as the dynamics of massless charged particles, the infinite energy of the electromagnetic field, and the limits of the Green’s function method. Presenting a rich, multilayered, and critical exposition on the electromagnetic paradigm underlying the whole Universe, the book offers a valuable resource for researchers and graduate students in theoretical physics alike.

Cosmology has become a very active research field in the last decades thanks to the impressing improvement of our observational techniques which have led to landmark discoveries such as the accelerated expansion of the universe, and have put physicists in front of new mysteries to unveil, such as the quest after the nature of dark matter and dark energy. These notes offer an approach to cosmology, covering fundamental topics in the field: the expansion of the universe, the thermal history, the evolution of small cosmological perturbations and the anisotropies in the cosmic microwave background radiation. Some extra topics are presented in the penultimate chapter and some standard results of physics and mathematics are available in the last chapter in order to provide a self-contained treatment. These notes offer an in-depth account of the above-mentioned topics and are aimed to graduate students who want to build an expertise in cosmology.

The purpose of this book is twofold: first, it sets out to equip the reader with a sound understanding of the foundations of probability theory and stochastic processes, offering step-by-step guidance from basic probability theory to advanced topics, such as stochastic differential equations, which typically are presented in textbooks that require a very strong mathematical background. Second, while leading the reader on this journey, it aims to impart the knowledge needed in order to develop algorithms that simulate realistic physical systems. Connections with several fields of pure and applied physics, from quantum mechanics to econophysics, are provided. Furthermore, the inclusion of fully solved exercises will enable the reader to learn quickly and to explore topics not covered in the main text. The book will appeal especially to graduate students wishing to learn how to simulate physical systems and to deepen their knowledge of the mathematical framework, which has very deep connections with modern quantum field theory.

This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schrödinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.

This book presents the basic elements of Analytical Mechanics, starting from the physical motivations that favor it with respect to the Newtonian Mechanics in Cartesian coordinates. Rather than presenting Analytical Mechanics mainly as a formal development of Newtonian Mechanics, it highlights its effectiveness due to the following five important achievements: 1) the most economical description of time evolution in terms of the minimal set of coordinates, so that there are no constraint forces in their evolution equations; 2) the form invariance of the evolution equations, which automatically solves the problem of fictitious forces; 3) only one scalar function encodes the formulation of the dynamics, rather than the full set of vectors which describe the forces in Cartesian Newtonian Mechanics; 4) in the Hamiltonian formulation, the corresponding evolution equations are of first order in time and are fully governed by the Hamiltonian function (usually corresponding to the energy); 5) the emergence of the Hamiltonian canonical algebra and its effectiveness in simplifying the control of the dynamical problem (e.g. the constant of motions identified by the Poisson brackets with the Hamiltonian, the relation between symmetries and conservations laws, the use of canonical transformations to reduce the Hamiltonian to a simpler form etc.). The book also addresses a number of points usually not included in textbook presentations of Analytical Mechanics, such as 1) the characterization of the cases in which the Hamiltonian differs from the energy, 2) the characterization of the non-uniqueness of the Lagrangian and of the Hamiltonian and its relation to a “gauge” transformation, 3) the Hamiltonian formulation of the Noether theorem, with the possibility that the constant of motion corresponding to a continuous symmetry of the dynamics is not the canonical generator of the symmetry transformation but also involves the generator of a gauge transformation. In turn, the book’s closing chapter is devoted to explaining the extraordinary analogy between the canonical structure of Classical and Quantum Mechanics. By correcting the Dirac proposal for such an explanation, it demonstrates that there is a common Poisson algebra shared by Classical and Quantum Mechanics, the differences between the two theories being reducible to the value of the central variable of that algebra.

This book presents a large collection of problems in Quantum Mechanics that are solvable within a limited time and using simple mathematics. The problems test both the student’s understanding of each topic and their ability to apply this understanding concretely. Solutions to the problems are provided in detail, eliminating only the simplest steps. No problem has been included that requires knowledge of mathematical methods not covered in standard courses, such as Fuchsian differential equations. The book is in particular designed to assist all students who are preparing for written examinations in Quantum Mechanics, but will also be very useful for teachers who have to pose problems to their students in lessons and examinations.

This book presents a large collection of problems in Quantum Mechanics that are solvable within a limited time and using simple mathematics. The problems test both the student’s understanding of each topic and their ability to apply this understanding concretely. Solutions to the problems are provided in detail, eliminating only the simplest steps. No problem has been included that requires knowledge of mathematical methods not covered in standard courses, such as Fuchsian differential equations. The book is in particular designed to assist all students who are preparing for written examinations in Quantum Mechanics, but will also be very useful for teachers who have to pose problems to their students in lessons and examinations.

This book presents 140 problems with solutions in introductory nuclear and particle physics. Rather than being only partially provided or simply outlined, as is typically the case in textbooks on nuclear and particle physics, all solutions are explained in detail. Furthermore, different possible approaches are compared. Some of the problems concern the estimation of quantities in realistic experimental situations. In general, solving the problems does not require a substantial mathematics background, and the focus is instead on developing the reader’s sense of physics in order to work out the problem in question. Consequently, sections on experimental methods and detection methods constitute a major part of the book. Given its format and content, it offers a valuable resource, not only for undergraduate classes but also for self-assessment in preparation for graduate school entrance and other examinations.

This book presents 140 problems with solutions in introductory nuclear and particle physics. Rather than being only partially provided or simply outlined, as is typically the case in textbooks on nuclear and particle physics, all solutions are explained in detail. Furthermore, different possible approaches are compared. Some of the problems concern the estimation of quantities in realistic experimental situations. In general, solving the problems does not require a substantial mathematics background, and the focus is instead on developing the reader’s sense of physics in order to work out the problem in question. Consequently, sections on experimental methods and detection methods constitute a major part of the book. Given its format and content, it offers a valuable resource, not only for undergraduate classes but also for self-assessment in preparation for graduate school entrance and other examinations.

This book is exceptional in offering a thorough but accessible introduction to calorimetry that will meet the needs of both students and researchers in the field of particle physics. It is designed to provide the sound knowledge of the basics of calorimetry and of calorimetric techniques and instrumentation that is mandatory for any physicist involved in the design and construction of large experiments or in data analysis. An important feature is the correction of a number of persistent common misconceptions. Among the topics covered are the physics and development of electromagnetic showers, electromagnetic calorimetry, the physics and development of hadron showers, hadron calorimetry, and calibration of a calorimeter. Two chapters are devoted to more promising calorimetric techniques for the next collider. Calorimetry for Collider Physics, an introduction will be of value for all who are seeking a reliable guide to calorimetry that occupies the middle ground between the brief chapter in a generic book on particle detection and the highly complex and lengthy reference book.

This book is exceptional in offering a thorough but accessible introduction to calorimetry that will meet the needs of both students and researchers in the field of particle physics. It is designed to provide the sound knowledge of the basics of calorimetry and of calorimetric techniques and instrumentation that is mandatory for any physicist involved in the design and construction of large experiments or in data analysis. An important feature is the correction of a number of persistent common misconceptions. Among the topics covered are the physics and development of electromagnetic showers, electromagnetic calorimetry, the physics and development of hadron showers, hadron calorimetry, and calibration of a calorimeter. Two chapters are devoted to more promising calorimetric techniques for the next collider. Calorimetry for Collider Physics, an introduction will be of value for all who are seeking a reliable guide to calorimetry that occupies the middle ground between the brief chapter in a generic book on particle detection and the highly complex and lengthy reference book.

Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction,  classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland andRuijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.

Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction,  classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland andRuijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.

This textbook provides a sound foundation in physical optics by covering key concepts in a rigorous but accessible manner. Propagation of electromagnetic waves is examined from multiple perspectives, with explanation of which viewpoints and methods are best suited to different situations. After an introduction to the theory of electromagnetism, reflection, refraction, and dispersion, topics such as geometrical optics, interference, diffraction, coherence, laser beams, polarization, crystallography, and anisotropy are closely examined. Optical elements, including lenses, mirrors, prisms, classical and Fabry-Perot interferometers, resonant cavities, multilayer dielectric structures, interference and spatial filters, diffraction gratings, polarizers, and birefringent plates, are treated in depth. The coverage also encompasses such seldom-covered topics as modeling of general astigmatism via 4x4 matrices, FFT-based numerical methods, and bianisotropy, with a relativistic treatment of optical activity and the Faraday and Fresnel-Fizeau effects. Finally, the history of optics is discussed.

This textbook provides a sound foundation in physical optics by covering key concepts in a rigorous but accessible manner. Propagation of electromagnetic waves is examined from multiple perspectives, with explanation of which viewpoints and methods are best suited to different situations. After an introduction to the theory of electromagnetism, reflection, refraction, and dispersion, topics such as geometrical optics, interference, diffraction, coherence, laser beams, polarization, crystallography, and anisotropy are closely examined. Optical elements, including lenses, mirrors, prisms, classical and Fabry-Perot interferometers, resonant cavities, multilayer dielectric structures, interference and spatial filters, diffraction gratings, polarizers, and birefringent plates, are treated in depth. The coverage also encompasses such seldom-covered topics as modeling of general astigmatism via 4x4 matrices, FFT-based numerical methods, and bianisotropy, with a relativistic treatment of optical activity and the Faraday and Fresnel-Fizeau effects. Finally, the history of optics is discussed.

This textbook offers a readily comprehensible introduction to classical Newtonian gravitation, which is fundamental for an understanding of classical mechanics and is particularly relevant to Astrophysics. The opening chapter recalls essential elements of vectorial calculus, especially to provide the formalism used in subsequent chapters. In chapter two Classical Newtonian gravity theory for one point mass and for a generic number N of point masses is then presented and discussed. The theory for point masses is naturally extended to the continuous case. The third chapter addresses the paradigmatic case of spherical symmetry in the mass density distribution (central force), with introduction of the useful tool of qualitative treatment of motion. Subsequent chapters discuss the general case of non-symmetric mass density distribution and develop classical potential theory, with elements of harmonic theory, which is essential to understand the potential development in series of the gravitational potential, the subject of the fourth chapter. Finally, in the last chapter the specific case of motion of a satellite around the earth is considered. Examples and exercises are presented throughout the book to clarify aspects of the theory. The book is aimed at those who wish to progress further beyond an initial bachelor degree, onward to a master degree, and a PhD. It is also a valuable resource for postgraduates and active researchers in the field.

This textbook offers a readily comprehensible introduction to classical Newtonian gravitation, which is fundamental for an understanding of classical mechanics and is particularly relevant to Astrophysics. The opening chapter recalls essential elements of vectorial calculus, especially to provide the formalism used in subsequent chapters. In chapter two Classical Newtonian gravity theory for one point mass and for a generic number N of point masses is then presented and discussed. The theory for point masses is naturally extended to the continuous case. The third chapter addresses the paradigmatic case of spherical symmetry in the mass density distribution (central force), with introduction of the useful tool of qualitative treatment of motion. Subsequent chapters discuss the general case of non-symmetric mass density distribution and develop classical potential theory, with elements of harmonic theory, which is essential to understand the potential development in series of the gravitational potential, the subject of the fourth chapter. Finally, in the last chapter the specific case of motion of a satellite around the earth is considered. Examples and exercises are presented throughout the book to clarify aspects of the theory. The book is aimed at those who wish to progress further beyond an initial bachelor degree, onward to a master degree, and a PhD. It is also a valuable resource for postgraduates and active researchers in the field.

This book offers a comprehensive overview of thermodynamics. It is divided into four parts, the first of which equips readers with a deeper understanding of the fundamental principles of thermodynamics of equilibrium states and of their evolution. The second part applies these principles to a series of generalized situations, presenting applications that are of interest both in their own right and in terms of demonstrating how thermodynamics, as a theory of principle, relates to different fields. In turn, the third part focuses on non-equilibrium configurations and the dynamics of natural processes. It discusses both discontinuous and continuous systems, highlighting the interference among non-equilibrium processes, and the nature of stationary states and of fluctuations in isolated systems. Lastly, part four introduces the relation between physics and information theory, which constitutes a new frontier in fundamental research.The book includes step-by-step exercises, with solutions, to help readers to gain a fuller understanding of the subjects, and also features a series of appendices providing useful mathematical formulae. Reflecting the content of modern university courses on thermodynamics, it is a valuable resource for students and young scientists in the fields of physics, chemistry, and engineering.

This book offers a comprehensive overview of thermodynamics. It is divided into four parts, the first of which equips readers with a deeper understanding of the fundamental principles of thermodynamics of equilibrium states and of their evolution. The second part applies these principles to a series of generalized situations, presenting applications that are of interest both in their own right and in terms of demonstrating how thermodynamics, as a theory of principle, relates to different fields. In turn, the third part focuses on non-equilibrium configurations and the dynamics of natural processes. It discusses both discontinuous and continuous systems, highlighting the interference among non-equilibrium processes, and the nature of stationary states and of fluctuations in isolated systems. Lastly, part four introduces the relation between physics and information theory, which constitutes a new frontier in fundamental research.The book includes step-by-step exercises, with solutions, to help readers to gain a fuller understanding of the subjects, and also features a series of appendices providing useful mathematical formulae. Reflecting the content of modern university courses on thermodynamics, it is a valuable resource for students and young scientists in the fields of physics, chemistry, and engineering.

This book seeks to bridge the gap between the parlance, the models, and even the notations used by physicists and those used by mathematicians when it comes to the topic of probability and stochastic processes. The opening four chapters elucidate the basic concepts of probability, including probability spaces and measures, random variables, and limit theorems. Here, the focus is mainly on models and ideas rather than the mathematical tools. The discussion of limit theorems serves as a gateway to extensive coverage of the theory of stochastic processes, including, for example, stationarity and ergodicity, Poisson and Wiener processes and their trajectories, other Markov processes, jump-diffusion processes, stochastic calculus, and stochastic differential equations. All these conceptual tools then converge in a dynamical theory of Brownian motion that compares the Einstein–Smoluchowski and Ornstein–Uhlenbeck approaches, highlighting the most important ideas that finally led to a connection between the Schrödinger equation and diffusion processes along the lines of Nelson’s stochastic mechanics. A series of appendices cover particular details and calculations, and offer concise treatments of particular thought-provoking topics.

This book seeks to bridge the gap between the parlance, the models, and even the notations used by physicists and those used by mathematicians when it comes to the topic of probability and stochastic processes. The opening four chapters elucidate the basic concepts of probability, including probability spaces and measures, random variables, and limit theorems. Here, the focus is mainly on models and ideas rather than the mathematical tools. The discussion of limit theorems serves as a gateway to extensive coverage of the theory of stochastic processes, including, for example, stationarity and ergodicity, Poisson and Wiener processes and their trajectories, other Markov processes, jump-diffusion processes, stochastic calculus, and stochastic differential equations. All these conceptual tools then converge in a dynamical theory of Brownian motion that compares the Einstein–Smoluchowski and Ornstein–Uhlenbeck approaches, highlighting the most important ideas that finally led to a connection between the Schrödinger equation and diffusion processes along the lines of Nelson’s stochastic mechanics. A series of appendices cover particular details and calculations, and offer concise treatments of particular thought-provoking topics.

This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion.  The rationale for providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authors’s lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.

This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion.  The rationale for providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authors’s lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.

This book is based on a series of lectures for an Astrophysics of the Interstellar Medium (ISM) master’s degree in Astrophysics and Cosmology at Padova University. From the cold molecular phase in which stars and planetary systems form, to the very hot coronal gas that surrounds galaxies and galaxy clusters, the ISM is everywhere. Studying its properties is vital for the exploration of virtually any field in astronomy and cosmology. These notes give the student a coherent and accurate mathematical and physical approach, with continuous references to the real ISM in galaxies. The book is divided into three parts. Part One introduces the equations of fluid dynamics for a system at rest and acoustic waves, and then explores the real ISM through the role of thermal conduction and viscosity, concluding with a discussion of shock waves and turbulence. In Part Two, the electromagnetic field is switched on and its role in modulating shock waves and contrasting gravity is studied. Part Three describes dust and its properties, followed by the main stellar sources of energy. The last two chapters respectively address the various components of the ISM and molecular clouds and star formation.

This book is based on a series of lectures for an Astrophysics of the Interstellar Medium (ISM) master’s degree in Astrophysics and Cosmology at Padova University. From the cold molecular phase in which stars and planetary systems form, to the very hot coronal gas that surrounds galaxies and galaxy clusters, the ISM is everywhere. Studying its properties is vital for the exploration of virtually any field in astronomy and cosmology. These notes give the student a coherent and accurate mathematical and physical approach, with continuous references to the real ISM in galaxies. The book is divided into three parts. Part One introduces the equations of fluid dynamics for a system at rest and acoustic waves, and then explores the real ISM through the role of thermal conduction and viscosity, concluding with a discussion of shock waves and turbulence. In Part Two, the electromagnetic field is switched on and its role in modulating shock waves and contrasting gravity is studied. Part Three describes dust and its properties, followed by the main stellar sources of energy. The last two chapters respectively address the various components of the ISM and molecular clouds and star formation.

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.

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.

This book offers a didactic introduction to light–matter interactions at both the classical and semi-classical levels. Pursuing an approach that describes the essential physics behind the functionality of any optical element, it acquaints students with the broad areas of optics and photonics. Its rigorous, bottom-up approach to the subject, using model systems ranging from individual atoms and simple molecules to crystalline and amorphous solids, gradually builds up the reader’s familiarity and confidence with the subject matter. Throughout the book, the detailed mathematical treatment and examples of practical applications are accompanied by problems with worked-out solutions. In short, the book provides the most essential information for any graduate or advanced undergraduate student wishing to begin their course of study in the field of photonics, or to brush up on important concepts prior to an examination.