Fundamentals of physics E-Book

Alessio Mangoni

• Herausgeber: Alessio Mangoni
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2020

Beschreibung

This book aims to provide solid bases for the study of physics for the university and it is divided into four parts, each dedicated to a fundamental branch of physics: quantum mechanics, theoretical physics, particle physics and condensed matter physics. In the first part we start with the concept of wave function, until the Heisenberg uncertainty principle. In the second part, after recalling the basic concepts of relativity, we treat the elementary particles and the hadrons, arriving to the notions of scattering and cross section. The third part is dedicated to the theoretical physics, where we analyze the field theory and the concepts of Lagrangian and Hamiltonian, introducing the quantum electrodynamics (QED), passing through the Klein-Gordon, Dirac and Maxwell fields. In the last part of the book we expose the basics of the condensed matter physics, including diffusion and Brownian motion, Drude and Sommerfeld models, the calculation of specific heat and the principal mechanical properties of solids, with references to lattice defects and semiconductors.

Leseprobe

Contents

Contents

Introduction

Part I

Quantum Mechanics

Introduction

The wave function

The Schrödinger equation

Free particle equation

General equation

Continuity equation

Wave packets

Normalization

Fourier transform

Interval of length 2pi

Interval of length L

Infinite interval

Coordinate and momentum space

Expectation value

Operators

Position operator

Momentum operator

Energy operator

Angular momentum operator

Spherical coordinates

Commutation relations

Uncertainty principle

Eigenvalue equations

Position operator

Momentum operator

The third component of angular momentum operator

Part II

Particle Physics

Introduction

Natural units

Bases of relativity

Four-vectors

Lorentz transformations

Relativistic kinematics

Invariant mass

Particles

Elementary particles

Quarks

Leptons

Quark model

Fundamental interactions

Hadrons

Mesons

The Yukawa meson

Baryons

Nucleons

Cosmic rays

The pion

The muon

Particles with strangeness

Kaons

Hyperons

Energy loss

Ionization energy loss

Electron energy loss

Photon energy loss

Hadron energy loss

Quantum numbers and symmetries

The strangeness

The parity

Parity of the photon

Parity of a two-particle system

Charge conjugation

Charge conjugation of the photon

Charge conjugation of the pion

Time reversal

CPT theorem

Baryon number

Lepton number

Isospin

Hypercharge

The Gell-Mann-Nishijima formula

G-parity

Helicity

Chirality

Scattering and decays

Reference frames

The invariant quantity s

Mandelstam variables

Two‐body elastic scattering

Fermi's golden rule

Cross section

Beam intensity reduction

Luminosity

Two-body cross section

Decays

Part III

Theoretical Physics

Introduction

Lagrangian and Hamiltonian

Lagrangian field theory

Hamiltonian field theory

Symmetries and gauge invariance

Symmetries and conservation laws

Gauge invariance

Campo di Klein-Gordon

The Klein-Gordon field

Klein-Gordon Lagrangian

Klein-Gordon Hamiltonian

The electromagnetic field

Maxwell's equations

Gauge invariance

Maxwell Lagrangian

The Dirac field

Dirac equation

Properties of gamma matrices

Dirac Lagrangian

Dirac Hamiltonian

Free particle solutions

Quantum electrodynamics

Interaction Lagrangian

Interaction Hamiltonian

Field operators

The S matrix

Part IV

Condensed Matter Physics

Introduction

Brownian motion and diffusion

Introduction

Einstein relation

Fick's laws

Random walker

Langevin equation

Fokker-Planck equation

Boltzmann equation

Drude model

Introduction

Electric conductivity

Hall effect

Thermal conductivity

Seebeck effect

Sommerfeld model

Quantum treatment

Internal energy

Sommerfeld expansion

Mechanical properties of solids

Introduction

Young's modulus

Poisson's ratio

Lattice defects

Introduction

Point defects

Color centers

Dislocations

Semiconductors

Intrinsic semiconductor

Extrinsic semiconductor

 

Wave packets

We have seen that the general solution of the Schrödinger equation for a free particle (i.e. where V=0) is given by an overlap of plane waves, each with a certain wave number k. A free particle with a well-defined k (or, equivalently, a well-defined momentum p) has the following wave function