Bücher der Reihe UNITEXT for Physics

Based on a series of university lectures on nonrelativistic quantum mechanics, this textbook covers a wide range of topics, from the birth of quantum mechanics to the fine-structure levels of heavy atoms.

This book introduces the basic concepts of particle cosmology and covers all the main aspects of the Big Bang Model (expansion of the Universe, Big Bang Nucleosynthesis, Cosmic Microwave Background, large scale structures) and the search for new physics (inflation, baryogenesis, dark matter, dark energy).

This textbook, now in its third edition, provides a formative introduction to the structure of matter that will serve as a sound basis for students proceeding to more complex courses, thus bridging the gap between elementary physics and topics pertaining to research activities.

This book offers a self-contained introduction to the theory of electroweak interactions based on the semi-classical approach to relativistic quantum field theory, with thorough discussion of key aspects of the field.

This textbook offers an advanced undergraduate or initial graduate level introduction to topics such as kinetic theory, equilibrium statistical mechanics and the theory of fluctuations from a modern perspective.

This introduction to Hilbert space will equip the reader for more demanding further study. It builds a pedagogic bridge between the rigorous style of mathematics and the more practical perspective of physicists.

Quantum Physics of Light and Matter

This book describes the basic physical principles of atomic spectroscopy and the absorption and emission of radiation in astrophysical and laboratory plasmas.

The book examines the basic physical principles of atomic spectroscopy and the absorption and emission of radiation in astrophysical and laboratory plasmas. Each chapter starts with simple physical situations and then considers more complicated models.

Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result.

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 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.

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.

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 basic introduction to quantum mechanics. An attempt has been made to anticipate the conceptual problems students encounter when they first study quantum mechanics. The goal of the presentation is to provide the students with a solid background in quantum mechanics.

This textbook introduces readers to the detailed and methodical resolution of classical and more recent problems in analytical mechanics. This valuable learning tool includes worked examples and 40 exercises with step-by-step solutions, carefully chosen for their importance in classical, celestial and quantum mechanics. The collection comprises six chapters, offering essential exercises on: (1) Lagrange Equations; (2) Hamilton Equations; (3) the First Integral and Variational Principle; (4) Canonical Transformations; (5) Hamilton - Jacobi Equations; and (6) Phase Integral and Angular FrequenciesEach chapter begins with a brief theoretical review before presenting the clearly solved exercises. The last two chapters are of particular interest, because of the importance and flexibility of the Hamilton-Jacobi method in solving many mechanical problems in classical mechanics, as well as quantum and celestial mechanics.Above all, the book provides students and teachers alike with detailed, point-by-point and step-by-step solutions of exercises in Lagrangian and Hamiltonian mechanics, which are central to most problems in classical physics, astronomy, celestial mechanics and quantum physics.

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.

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 new edition includes the latest developments in the treatment of strongly interacting two-dimensional electrons and discusses the generalization from small to larger systems.The book provides explanations in a class-tested tutorial style, and each chapter includes problems reviewing key concepts and calculations.

This book presents a basic introduction to quantum mechanics. An attempt has been made to anticipate the conceptual problems students encounter when they first study quantum mechanics. The goal of the presentation is to provide the students with a solid background in quantum mechanics.

L¿invenzione dellaser ha generato una vera rivoluzione nella scienza e nella tecnologia e hadato luogo alla nascita di una nuova disciplina chiamata Fotonica. Le applicazionidella Fotonica che hanno un impatto cruciale in molti ambiti della nostra vitasono le comunicazioni in fibra ottica su cui si basa il funzionamento diInternet e del traffico telefonico su grandi distanze, i dischi ottici (CD,DVD, Blu-ray), la sensoristica ottica di tipo industriale e ambientale, lalavorazione dei materiali e la chirurgia con il laser, l¿illuminazione con i LED.Questa secondaedizione contiene diversi ampliamenti e modifiche al testo pubblicato nel 2012,che ha colmato un vuoto nel panorama italiano di testi universitari riguardantila Fotonica. Dopo avere esposto in modo sintetico ma rigoroso i concetti chestanno alla base del funzionamento del laser e della propagazione della lucenella materia, sono descritti i principali componenti e dispositivi ottici eoptoelettronici, quali le fibre ottiche, gli amplificatori, i modulatori e irivelatori. Il capitolo finale fornisce anche cenni sulle principaliapplicazioni. In coda a tutti i capitoli, tranne l¿ultimo, sono proposti degliesercizi. Il livello della trattazione e la scelta degli argomenti rendono iltesto particolarmente adatto a un corso semestrale per studenti di Ingegneria edi Fisica, ma il volume può essere utile più in generale per dottorandi,ricercatori e progettisti che desiderino un¿introduzione agile ai concetti e aimetodi della Fotonica.

Questo eserciziario nasce dalla raccolta di problemi d'esame assegnati agli studenti del corso di Struttura della Materia, che si colloca al confine fra il Corso Triennale e quello Magistrale. Alla fine di ciascun capitolo si trova un riepilogo ragionato di formule utili, e l¿ultima parte del volume è dedicata alle unità di misura, alle formule di Meccanica Quantistica e alle tecniche per manipolare il momento angolare, i metodi variazionale e quello perturbativo elementare. Quasi tutti i problemi sono applicazioni della Meccanica Quantistica, anche se si utilizzano nozioni di Termodinamica, Meccanica ed Elettromagnetismo. I problemi di questo manuale differiscono rispetto a quelli che caratterizzano libri di Fisica Teorica (che possono anche essere astratti o rilevanti per l'Astrofisica o le Interazioni Deboli, soprattutto nel fatto che) soprattutto nel fatto che questi devono alla fine determinare dei valori realistici di misure standard su atomi molecole o solidi. In Fisica, la conoscenza di ogni argomento è sempre operativa, cioè comporta l'abilità di risolvere problemi; ma di solito non basta mettere i dati in qualche formula risolutiva. Lo studente deve riconoscere nel problema una fattispecie della teoria generale, e questo può essere arduo. Però un problema abbastanza impegnativo da richiedere una comprensione approfondita della materia non implica necessariamente una soluzione lunga ed elaborata. In questo volume gli Autori si sono proposti di presentare esercizi, ciascuno dei quali può essere svolto con pochi calcoli, tipicamente in un'ora. Tuttavia per lo studente essi rappresentano una significativa verifica della sua preparazione. La formulazione, che in alcuni problemi è modellistica, ha il pregio di evidenziare gli aspetti concettuali. I procedimenti proposti spesso non sono unici e il lettore potrebbe escogitarne altri ugualmente validi.

Questo libro trae la sua origine dagli appunti preparati per le lezioni di Metodi Matematici della Fisica tenute al Dipartimento di Fisica dell'Università di Pisa, e via via sistemati, raffinati e aggiornati nel corso di molti anni di insegnamento. L'intento generale è di fornire una presentazione per quanto possibile semplice e diretta dei metodi matematici basilari e rilevanti per la Fisica. Anche allo scopo di mantenere questo testo entro i limiti di un manuale di dimensioni contenute e di agevole consultazione, sono stati spesso sacrificati i dettagli tecnici delle dimostrazioni matematiche (o anzi le dimostrazioni per intero) e anche i formalismi eccessivi, che tendono a nascondere la vera natura dei problemi. Al contrario, si è cercato di evidenziare ¿ per quanto possibile ¿ le idee sottostanti e le motivazioni che conducono ai diversi procedimenti. L'obiettivo principale e quello di mettere in condizione chi ha letto questo libro di acquisire gli strumenti adatti e le conoscenze di base che gli permettano di affrontare senza difficoltà anche testi più avanzati e impegnativi. Questa nuova Edizione conserva la struttura generale della prima Edizione, ma è arricchita dall'inserimento di numerosi esempi (e controesempi), con nuove osservazioni e chiarimenti su tutti gli argomenti proposti: Serie di Fourier, Spazi di Hilbert, Operatori lineari, Funzioni di Variabile complessa, Trasformate di Fourier e di Laplace, Distribuzioni. Inoltre, le prime nozioni della Teoria dei Gruppi, delle Algebre di Lie e delle Simmetrie in Fisica (che erano confinate in una Appendice nella Prima Edizione) vengono ora proposte in una forma sensibilmente ampliata, con vari esempi in vista delle applicazioni alla Fisica. In particolare, due nuovi Capitoli sono dedicati allo studio delle proprietà di simmetria dell'atomo di idrogeno e dell'oscillatore armonico in Meccanica Quantistica.