Course detail

Modern Physics

FEKT-MKC-MFYAcad. year: 2023/2024

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


Number of ECTS credits


Mode of study

Not applicable.

Entry knowledge

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

Rules for evaluation and completion of the course

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.


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

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Lubomír Skála: Úvod do kvantové mechaniky ACADEMIA 2005
House J.E.: Fundamentals of Quantum Mechanics Academic Press, San Diego, London,..., 1998
Landshoff P., Metherell A.,Rees G.: Essential Quantum Physics Cambridge University Press,1999
Formánek J. : Úvod do kvantové teorie I, II, ACADEMIA, 2004 druhé rozšířené vydání.
Sartori L.: Understanding Relativity University of California Press, Berkeley, Los Angeles, London, 1996

Recommended reading

L.Eckertová: Cesty poznávání ve fyzice Prometheus Praha 2004
Halliday D., Resnick R., Walker J.: Fyzika Vysoké učení technické v Brně Vutium, Prometheus Praha 2000
Serway R., A.: Physics for Scientists and Engineers with Modern Physics Saunders College Publishing, Philadelphia, London,..., 1996


Classification of course in study plans

  • Programme MKC-EEN Master's, 1. year of study, winter semester, compulsory-optional

Type of course unit



39 hours, optionally

Teacher / Lecturer


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 hours, compulsory

Teacher / Lecturer


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.