Course detail

Modern Physics

FEKT-MPA-MFYAcad. year: 2022/2023

The postulates of relativity and their implications, the Lorentz transformation, world lines, relativistic energy and momentum. Quantization of energy, wave properties of particles, the uncertainty principle, Hermitian operators, Schrödinger equation, particles in potential fields, tunneling through a barrier, spin, principles of a laser, radiative transitions, band theory of solids.

Language of instruction

English

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Karel Liedermann, CSc.

Department

Department of Physics (UFYZ)

Learning outcomes of the course unit

Students will have some familiarity with main ideas of relativity, with most of the important models of quantum mechanics and with theory of deterministic chaos.

Prerequisites

The subject knowledge on the Bachelor´s degree level is requested.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods include lectures and seminars. The course is supoported by an e-learning system, which is, however, used as a repository of lectures and examples only. Students have to write a homework, consisting in solving a single project/assignment independently during the course.

Assesment methods and criteria linked to learning outcomes

30 points - numerical exercises.
70 points - final exam.

Course curriculum

The postulates of relativity and their implications, the Lorentz transformation, world lines, relativistic energy and momentum. The quantization of energy, the wave properties of particles, the uncertainty principle, Hermitian operators, Schrödinger equation, particles in boxes, tunneling through a barrier, spin, radiative transitions, the band theory.
Chaos in conservative and dissipative systems, deterministic chaos.

Work placements

Not applicable.

Aims

The purpose of this course is to introduce students to the most important ideas, concepts and laws of twentieth-century physics.

Specification of controlled education, way of implementation and compensation for absences

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Griffiths, D., J.: Introduction to Quantum Mechanics, Cambridge University Press; 3 edition, 2018, ISBN: 978-1107189638 (EN)
Sartori, L.: Understanding Relativity, University of California Press, Berkeley, 1996, ISBN: 978-0520200296 (EN)
Sherwin, C., H.: Introduction to Quantum Mechanics, New Academic Science Ltd, 2018, ISBN: 978-1781831083 (EN)

Recommended reading

Sakurai, J., J., Napolitano, J., J.: Modern Quantum Mechanics, 2 edition, Pearson, 2010, ISBN: 978-0805382914 (EN)

Classification of course in study plans

  • Programme MPAD-BIO Master's 2 year of study, winter semester, compulsory-optional
  • Programme MPA-EAK Master's 1 year of study, winter semester, compulsory-optional
  • Programme MPA-EEN Master's 1 year of study, winter semester, compulsory-optional
  • Programme MPA-MEL Master's 1 year of study, winter semester, compulsory-optional
  • Programme MPAD-MEL Master's 1 year of study, winter semester, compulsory-optional

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

doc. Ing. Karel Liedermann, CSc.

Syllabus

The Principle of Relativity, the Michelson-Morley Experiment, the Postulates of Special Relativity and their Implications.
The Lorentz Transformation. Some Consequences of the Transformation Equations, the Transformation of Velocity.
World Lines. Relativistic Energy and Momentum.
Photons, Tachyons. The Main Ideas of General Relativity. Paradoxes of Relativity.
Blackbody Radiation, the Photoelectric Effect, the Compton Effect.
The Bohr Model for the Hydrogen Atom. The Wave Properties of Particles, the Uncertainty Principle, the Wave Function.
Hermitian Operators, Eigenvalues and Eigenfunctions of Operators.
The Schrödinger Equation,the Particle in a One-Dimensional Box, the Linear Harmonic Oscillator.
Tunneling through a Barrier, the Scanning Tunneling Microscope. Tunneling and Superconductivity. The Hydrogen Atom.
The Zeeman Effect, Spin, the Pauli Exclusion Principle.
Radiative Transitions, Absorption, Spontaneous and Stimulated Emission, Lasers.
Free-Electron Theory of Metals, the Fermi-Dirac Distribution Function, Band Theory of Solids.
Chaos in Conservative Systems, Deterministic Chaos.

Fundamentals seminar

13 hod., compulsory

Teacher / Lecturer

doc. Ing. Karel Liedermann, CSc.

Syllabus

Implications of the Postulates of Relativity:Simultaneity, Time Dilation, Length Contraction.
The Lorentz Transformation. Transformation of Velocity.
Space-Time Diagrams.
Relativistic Momentum and Energy.
Planck´s Law, the Photoelectric Effect, the Compton Effect.
The Bohr Model for the Hydrogen Atom. The Uncertainty Principle.
Eigenvalues and Eigenfunctions of Operators. Hermitian Operators.
The Schrödinger Equation. Particles in Boxes.
The Phenomenon of Barrier Penetration.
The Hydrogen Atom.
The Zeeman Effect, Spin.
The Fermi-Dirac Distribution Function.