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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.

This textbook introduces the language and the techniques of the theory of dynamical systems of finite dimension for an audience of physicists, engineers, and mathematicians at the beginning of graduation. Author addresses geometric, measure, and computational aspects of the theory of dynamical systems. Some freedom is used in the more formal aspects, using only proofs when there is an algorithmic advantage or because a result is simple and powerful. The first part is an introductory course on dynamical systems theory. It can be taught at the master's level during one semester, not requiring specialized mathematical training. In the second part, the author describes some applications of the theory of dynamical systems. Topics often appear in modern dynamical systems and complexity theories, such as singular perturbation theory, delayed equations, cellular automata, fractal sets, maps of the complex plane, and stochastic iterations of function systems are briefly explored for advanced students. The author also explores applications in mechanics, electromagnetism, celestial mechanics, nonlinear control theory, and macroeconomy. A set of problems consolidating the knowledge of the different subjects, including more elaborated exercises, are provided for all chapters.

This book presents 140 problems with solutions in introductory nuclear and particle physics. 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.

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 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 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 book offers 242 solved problems of varying difficulty in nonrelativistic quantum mechanics, from themes of the crisis of classical physics through modern atomic physics to intriguing aspects of the EPR paradox and more.

This up-to-date, self-contained review of the theory of gravitational interactions presents a traditional introduction, then discuss analogies and differences between a geometric theory of gravity and the gauge theories of the other fundamental interactions.

This textbook presents the established sciences of optical, infrared, and radio astronomy as distinct research areas, focusing on the science targets and the constraints that they place on instrumentation in the different domains.

This textbook presents ultraviolet and X-ray astronomy, gamma-ray astronomy, cosmic ray astronomy, neutrino astronomy, and gravitational wave astronomy as distinct research areas, focusing on the astrophysics targets and the requirements with respect to instrumentation and observation methods.

This book offers an excellent introduction to General Relativity and Cosmology. In the first part, the main concepts of General Relativity are presented, while the second offers an introduction to the astrophysical applications.

This book, now in its second edition, provides an introductory course on theoretical particle physics with the aim of filling the gap that exists between basic courses of classical and quantum mechanics and advanced courses of (relativistic) quantum mechanics and field theory.

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 uses less strict yet still formal mathematical language to clarify a variety of concepts in Quantum Field Theory that remain somewhat "fuzzy" in many books designed for undergraduates and fresh graduates.

Here is an introduction to contemporary plasma physics that discusses recent advances in the field and covers a careful choice of applications to various branches of astrophysics and space science. Includes chapter end exercises, suggestions and solutions.

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.

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

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 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.

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.

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.

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.