Courses on Mathematics and Physics of the bachelor previous to this course

OBJECTIVES: The Course on Modern Physics aims to provide an introduction to the basic pillars on which Modern Physics is based: the theories of relativity - special and general ¿ and the quantum mechanics. The former transformed our ideas about space, time and the universe. On the other hand, the quantum revolution changed our image of the atomic and subatomic world and, ultimately, of the intimate structure of matter. Some of the main scientific and technological consequences that derive from them, and that have contributed to transform our world, such as the atomic energy, lasers, semiconductor devices and computers, superconductivity, etc, will be also discussed.

PART I THEORY OF RELATIVITY 1 Postulates of the Special Theory of Relativity 1.1 Introduction 1.2 The Classical Relativity 1.2.1 The Galilean Principle of Relativity 1.2.2 The Galilean Transformation and Classical Mechanics 1.3 The Principle of Relativity and the Electromagnetic Theory 1.4 Einstein¿s Postulates 2 Relativistic Kinematics 2.1 Lorentz Transformation 2.1.1 Lorentz Transformation of Coordinates 2.1.2 Lorentz Velocity Transformation 2.3 Consequences of the Lorentz Transformation 2.3.1 Time Dilation 2.3.2 Contraction of Length 2.3.3 Relativity of Simultaneity 3 Relativistic Dynamics 3.1 Introduction 3.2 Relativistic Linear Momentum 3.3 Relativistic Expression of the Force 3.4 Relativistic Energy 3.4.1 Kinetic Energy 3.4.2 Definition of the Total Energy 3.4.3 Mass-Energy Equivalence 3.4.4 Energy-Momentum Relation 4 Introduction to the General Relativity 4.1 Introduction 4.2 Equivalence Principle 4.3 The Light in a Gravitational Field 4.4 Perihelion Precession of Mercury 4.5 Gravitational Redshift of Light 4.6 The Global Positioning System (GPS) 4.7 Black Holes PART II QUANTUM THEORY 5 The Birth of Quantum Physics. Wave ¿ Particle Duality 5.1 Introduction 5.2 Waves and Particles 5.3 The Nature of Light 5.3.1 Blackbody Radiation. Planck¿s Hypothesis 5.3.2 Photoelectric Effect. Photons 5.4 De Broglie Hypothesis. Electron Difraction. The Double Slit Experiment 6 Quantum Mechanics. Schrödinger Equation. Wave Function 6.1 The New Quantum Mechanics 6.2 Wave mechanics. Wave Function. Probabilistic Interpretation 6.3 The Schrödinger Equation 6.4 Time Independent Schrödinger Equation. Stationary States 6.5 One-dimensional Examples: 6.5.1 Particle in an Infinite Well Potential 6.5.2 The Harmonic Oscillator 6.6 Heisenberg Uncertainty Principle 7 Atoms and Molecules 7.1 Atomic Models. Bohr Model 7.2 Quantum Theory of the Hydrogen Atom. Quantum Numbers 7.3 Electron Spin. Pauli Exclusion Principle 7.4 Multielectronic Atoms. The Periodic Table 7.5 Spontaneous Emission and Stimulated Emission. The Laser 7.6 Molecules 7.6.1 The Ionic Bond 7.6.2 The Covalent Bond. Molecular Orbitals. Hybridation 8 The Solid State 8.1 Crystaline Solids 8.2 The Quantum Theory of Free Electrons in Metals 8.3 Band Theory of Solids. Conductors and Insulators 8.4 Semiconductors 8.4.1 Intrinsic and Extrinsic Semiconductors 8.4.2 Semiconductor Devices. The Diode and the Transistor 8.5 Superconductors 9 Electrons and Photons. Dirac Equation. Quantum Electrodynamics 9.1 Revolutions within the Revolution: the Dirac Equation. Consequences 9.1.1 Electron Spin 9.1.2 The Big Surprise: Antimatter 9.2 Quantum Electrodynamics. Virtual Photons and Electromagnetic Forces 10 Nuclear Physics 10.1 The Atomic Nucleus 10.2 Nuclear Stability. Radioactivity.The Radioactive Decay Law 10.3 Beta Disintegration. The Neutrino. The Weak Interaction 10.4 Yukawa and the Nuclear Forces. The Strong Interaction 11 Elementary Particles. The Structure of Matter 11.1 Elementary Particles. Accelerators and Colliders 11.2 The zoo of the Elementary Particles. Quarks 11.3 Quantum Chromodynamics 11.4 The Standard Model. Higgs Boson

* Lectures where the theoretical concepts are explained The lecturer will provide the following information (1 week in advance) - Main topics to be discussed during the session - Chapters/sections in each of the text books provided in the bibliography where the student can read about these topics * Activities for the solution of problems The main skills to be acquired in these activities are: - To understand the statement of a problem (for instance drawing an scheme that summarizes the statement) - To identify the physical phenomenon and the physical laws involved in the problem - To develop an strategy to reach the objective (for instance breaking the problem in small subproblems) - To be careful in the use of mathematics - To be able to make a critical analysis of the results (is the final number sensible?, are the dimensions consistent?) * Small tasks focused to search for scientific information from different sources (mainly internet) * Laboratoy sessions (~ 20 - 30 students divided in 2 people groups) The main skills to be developed in this activity are: - To understand that physics is an experimental science and that they can verify the laws that have been theoretically explained in the lectures - To use scientific instruments and to be careful in its operation - To be careful in the acquisiton of experimental data. - To learn the basis for the management of a scientific data set - To be able to write a report with the main results of the experiment - To be able to discuss in a critical way the experimental results: have we achieved the goals of the experiment? * Hours for individual tutorials will be set through Aula Global. It is possible to schedule sessions at other times by appointment with the lecturer