Introduction To The Basic Concepts Of Modern Physics

These notes are designed as a text book for a course on the Modern Physics Theory for undergraduate students. The purpose is providing a rigorous and self-contained presentation of the simplest theoretical framework using elementary mathematical tools. A number of examples of relevant applications and an appropriate list of exercises and answered questions are also given.

These notes are designed as a text book for a course on the Modern Physics Theory for undergraduate students. The purpose is providing a rigorous and self-contained presentation of the simplest theoretical framework using elementary mathematical tools. A number of examples of relevant applications and an appropriate list of exercises and answered questions are also given.

This is the third edition of a well-received textbook on modern physics theory. This book provides an elementary but rigorous and self-contained presentation of the simplest theoretical framework that will meet the needs of undergraduate students. In addition, a number of examples of relevant applications and an appropriate list of solved problems are provided.Apart from a substantial extension of the proposed problems, the new edition provides more detailed discussion on Lorentz transformations and their group properties, a deeper treatment of quantum mechanics in a central potential, and a closer comparison of statistical mechanics in classical and in quantum physics. The first part of the book is devoted to special relativity, with a particular focus on space-time relativity and relativistic kinematics. The second part deals with Schrödinger's formulation of quantum mechanics. The presentation concerns mainly one-dimensional problems, but some three-dimensional examples are discussed in detail. The third part addresses the application of Gibbs’ statistical methods to quantum systems and in particular to Bose and Fermi gases.

This is the third edition of a well-received textbook on modern physics theory. This book provides an elementary but rigorous and self-contained presentation of the simplest theoretical framework that will meet the needs of undergraduate students. In addition, a number of examples of relevant applications and an appropriate list of solved problems are provided.Apart from a substantial extension of the proposed problems, the new edition provides more detailed discussion on Lorentz transformations and their group properties, a deeper treatment of quantum mechanics in a central potential, and a closer comparison of statistical mechanics in classical and in quantum physics. The first part of the book is devoted to special relativity, with a particular focus on space-time relativity and relativistic kinematics. The second part deals with Schrödinger's formulation of quantum mechanics. The presentation concerns mainly one-dimensional problems, but some three-dimensional examples are discussed in detail. The third part addresses the application of Gibbs’ statistical methods to quantum systems and in particular to Bose and Fermi gases.

Introduction to the Basic Concepts of Modern Physics: Special Relativity, Quantum and Statistical Physics by Carlo Maria Becchi and Massimo D'EliaModern Physics, which is the subject of these notes, is well distinct fromClassical Physics, developed during the XIX century, and from ContemporaryPhysics, which was started during the Thirties (of XX century) and deals with thenature of Fundamental Interactions and with the physics of matter under extremeconditions. The aim of this introduction to Modern Physics is that of presenting aquantitative, even if necessarily also concise and schematic, account of the main features of Special Relativity, of Quantum Physics and of its application to theStatistical Theory of Matter. In usual textbooks these three subjects are presentedtogether only at an introductory and descriptive level, while analytic presentationscan be found in distinct volumes, also in view of examining quite complex technicalaspects. This state of things can be problematic from the educational point of view.Indeed, while the need for presenting the three topics together clearly followsfrom their strict interrelations (think for instance of the role played by specialrelativity in the hypothesis of de Broglie's waves or of that of statistical physics inthe hypothesis of energy quantization), it is also clear that this unitary presentationmust necessarily be supplied with enough analytic tools so as to allow a fullunderstanding of the contents and of the consequences of the new theories.On the other hand, since the present text is aimed to be introductory, the obviousconstraints on its length and on its prerequisites must be properly taken intoaccount: it is not possible to write an introductory encyclopedia. That imposes aselection of the topics which are most qualified from the point of view of thephysical content/mathematical formalism ratio.In the context of special relativity, after recalling the classical analysis of theether hypothesis, we introduce Lorentz's transformations and their action onMinkowski space-time, discussing the main consequences of the new interpretationof space and time. Then we introduce the idea of covariant formulation of the lawsof nature, considering in particular the new formulation of energy-momentumconservation. Finally, we discuss the covariant formulation of electrodynamics andits consequences on field transformation laws and Doppler effect.Regarding Schrödinger quantum mechanics, after presenting with some care theorigin of the wave equation and the nature of the wave function together with itsmain implications, like Heisenberg's Uncertainty Principle, we have emphasizedits qualitative consequences on energy levels. The main analysis begins withone-dimensional problems, where we have examined the origin of discrete energylevels and of band spectra as well as the tunnel effect. Extensions to more than onedimension have been limited to very simple examples in which the Schrödingerequation is easily separable, like the case of central forces. Among the simplestseparable cases we discuss the three-dimensional harmonic oscillator and the cubicwell with completely reflecting walls, which are however among the most usefulsystems for their applications to statistical physics. In a further section we havediscussed a general solution to the three-dimensional motion in a central potentialbased on the harmonic homogeneous polynomials in the Cartesian particle coor-dinates. This method, which simplifies the standard approach based on the analysisof the Schrödinger equation in spherical coordinates, is shown to be perfectlyequivalent to the standard one. It is applied in particular to the study of bound statesin spherical wells, of the hydrogen atom spectrum, of that of the isotropic harmonicoscillator and, finally, of elastic scattering.

This book is the second edition of an excellent undergraduate-level overview of classical and modern physics, intended for students of physics and related subjects, and also perfectly suited for the education of physics teachers. The twelve-chapter book begins with Newton’s laws of motion and subsequently covers topics such as thermodynamics and statistical physics, electrodynamics, special and general relativity, quantum mechanics and cosmology , the standard model and quantum chromodynamics. The writing is lucid, and the theoretical discussions are easy to follow for anyone comfortable with standard mathematics. An important addition in this second edition is a set of exercises and problems, distributed throughout the book. Some of the problems aim to complement the text, others to provide readers with additional useful tools for tackling new or more advanced topics. Furthermore, new topics have been added in several chapters; for example, the discovery of extra-solar planets from the wobble of their mother stars, a discussion of the Landauer principle relating information erasure to an increase of entropy, quantum logic, first order quantum corrections to the ideal gas equation of state due to the Fermi-Dirac and Bose-Einstein statistics. Both gravitational lensing and the time-correction in geo-positioning satellites are explained as theoretical applications of special and general relativity. The discovery of gravitational waves, one of the most important achievements of physical sciences, is presented as well. Professional scientists, teachers, and researchers will also want to have this book on their bookshelves, as it provides an excellent refresher on a wide range of topics and serves as an ideal starting point for expanding one’s knowledge of new or unfamiliar fields. Readers of this book will not only learn much about physics, they will also learn to love it.