Quantum, Nuclear and Particle Physics (bachelors)

In addition to the necessary assistive knowledge about determinants, matrices and the operations with them, the course is a classical introduction to linear algebra and analytical geometry with some elements of abstract algebra. Linear spaces, linear mappings, and the diagonalization of a matrix of an operator with simple spectrum are studied. After introducing the metric, Euclidean (unitary) spaces and linear operators are considered – symmetrical (Hermitian) and orthogonal (unitary) operators. The matrix of a symmetric linear operator is diagonalized by an orthogonal transformation. The course on analytical geometry includes vector algebra, straight lines in the plane, straight lines and planes in space, quadratic curves in the plane – including classification and transformation of the equations of such curves in canonical form, quadric surfaces.

This course covers the fundamentals of calculus: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences, and series of functions and uniformity. It shows not only the utility of abstract concepts, but also teaches an understanding in the construction of proofs, solving problems techniques, and application of the obtained knowledge in real geometric and physics problems.

The Classical Mechanics course covers fundamental principles governing the motion of particles and rigid bodies, starting with kinematics and progressing through dynamics and statics. Topics include Newton’s laws, conservation principles, translational and rotational motion, oscillations, and basic fluid dynamics, culminating in an exploration of wave phenomena. Through theoretical concepts and numerous practical examples, students will develop a deep understanding of classical mechanics and its applications in various scientific disciplines.

The course will provide basic knowledge of the UNIX-based working environments. A short description of the history of the operating systems is provided and the initial focus is on the text based user interface. It is used both as a command interpreter and as a scripting environment. During the course the students will understand the guiding principles of the operating systems, file systems, and networking. The basic principles of programming and algorithms are revealed. During the second half of the course, the main focus is a scientific programming language (C / C++ /Python or other, the choice depends on the lecturer). The topics include I/O possibilities of the chosen language, the basic algorithms, embedded data structures and their exploitation for computations in physics and other natural sciences.

The course presents differential calculus and integration of functions of multiple variables. The main topics are proceeded by analysis of Generalized Riemann integrals of unbounded functions as well as improper and Lebesgue integral combined with convergent series. It includes Fourier series, sufficient conditions for uniform convergence as well as Dirichlet condition for pointwise convergence.
The subject covers introduction of Euclidean spaces, open and closed sets, limits and partial derivatives. Taylor expansion of functions of several variables and analysis of their local and global properties is presented. The next main part of the course covers multiple integrals an their geometric meaning. Particular emphasis is given to line integrals (Green formula) and surface integrals (Stokes and Gauss-Ostrogradsky formulae).
The presentation is condensed and to facilitate the understanding and applications some proofs are omitted or simply sketched.

This course is the first of four courses that make up the core of mathematical methods of physics. Its main objective is to give the students the knowledge and mathematical techniques that are required for the next theoretical courses. Therefore, this first part of training on mathematical methods of physics is an introduction to complex analysis, consistent with the subsequent mathematical courses as well as courses in theoretical physics. Special attention is paid to clearly defining and clarifying the concepts and basic theorems, and the learning of practical procedures for solving problems in accordance with the needs of different sections of physics.

It’s an introductory course in probability and statistics for physicists. The aim is to make the students familiar with the basic concepts of probability and statistics and to show them how this knowledge could be used to perform data analysis. A lot of practical examples are covered during the lectures and the seminars.

The course represents a consistent presentation of the main concepts, values, laws, and experimental facts in the field of molecular physics and classical thermodynamics by using first year courses mathematical formalism. The simplest thermodynamic system, the ideal gas, is studied applying two complementary approaches (thermodynamic and molecular kinetic). Interparticle interactions are further considered within the Van der Waals equation for real gas modelling, recalculating the internal energy and exemplifying by studying the Joule-Thomson effect. First concepts of statistical physics are introduced through the entropy formulation of the Second principle, the Boltzmann and Maxwell-Boltzmann distributions. Basic principles of structure and macroscopic properties of liquids are studied, the first order phase transitions and the transfer phenomena in gases such as diffusion, internal friction, and thermal conductivity.

Course tutorials include solving problems from the major sections of the lecture course. In each section in the tutorials and in the individual student’s work, different types of problems, of variable levels of difficulty are solved. Furthermore, the fundamental thermodynamic laws and processes are applied and verified in practical demonstrations which help to better understand their physical nature and build capabilities to work with simple laboratory equipment, establish good laboratory practices of work.

In the last decade the Object-Oriented Programming paradigm and C++ programming language dominated in the scientific software in the field of Particle and Nuclear Physics and especially for analyzing data from LHC accelerator at CERN.  C++ is widely used programming language also for wide range of applications in numerous other fields. In this course, the students learn a language that has many practical uses in the real world.  The fundamental concepts of the object-oriented paradigm are introduced and object-oriented programming is stressed in place of traditional structured programming. The course is practically oriented, and lectures are well covered with practical exercises.

The basics of the vector and tensor algebra and analysis are considered. The course reflects the modern view of the vector and tensor calculus as a powerful tool to describe physical and geometrical objects. The students will acquire basic knowledge and computational skills which they will use in other courses and in their work as physicists

This course serves as an introduction to Ordinary Differential Equations (ODEs). It covers the fundamental concepts of ODEs, including the formulation of the main problem in the theory of ODEs. The course is designed to provide students with a comprehensive understanding of different kinds of ODEs and the methods for solving them. It also includes numerous problem sets to help students practice and apply their knowledge

The course in Electricity and Magnetism is the third part of the course in General Physics. It is designed for students in the third semester of their studies. The course is part of a longstanding tradition in the Department of Condensed Matter Physics.
The course consists of two main parts: i.) the general laws of electromagnetism and ii.) electrical and magnetic phenomena in matter. The first part contains three sections: 1) electrostatics; 2) stationary electric and magnetic fields and 3) alternating electromagnetic field. It is constructed on the principle of successive generalizations, allowing the students to get to Maxwell’s equations in an elegant and obvious way. Special attention is paid to the basic phenomena that are coded in Maxwell’s equations, such as the existence of, properties and physical characteristics of electromagnetic waves.
The second part concerns the electric and magnetic properties of matter in gas phase, plasma, electrolytes and metals. The model building in the case of dielectrics and plasma is based on classical physics, while for magnetism some quantum mechanical ideas (the quantization of magnetic moments) are explored. The plasma physics section is the only one in the general course dedicated to this most common state of matter.
Seminars deepen and illustrate with appropriate problems the lectures. Demonstrations of the discussed phenomena are also included in the syllabus.
During the sessions in the laboratory practice on electricity and magnetism, students of the second course deepen their experimental habits and skills to work with electric circuits. They gain experience of performing systematic electrical measurements and analysis of the results. At the same time, students build lasting habits for adherence to rules related to electrical safety techniques. At the same time, preparing for the exercises and their implementation, students acquire knowledge of important physical phenomena and laws of electricity and magnetism and interesting properties of condensed environments.
The laboratory practice on electricity and magnetism has a long tradition in the Department of Condensed Matter Physics. The acquired knowledge and skills are complementary to the preparation of the students of the second course in the subject “Electricity and magnetism”.

The course “Basic of Electronics” is a compulsory course, and it is an introduction to the basics of analogue and digital electronics – RF electronics, passive and active electronic elements, circuits and devices, electrical signals and their processing, logical elements, modern electronic technology etc. The course aims to build the basis of the understanding of electronic devices and to allow further advancements in more specialized topics like nuclear electronics. The course relies on close interaction with students and problem solving. The course provides electronic learning materials like lecture notes and books.
The laboratory exercises in the course cover different topics from the lectures and provide students with experience in building and analyzing simple circuits, and in various test instruments.

The basic facts, properties and techniques for solving partial differential equations are considered. The students will acquire basic knowledge and computational skills which they will use in other courses and in their work as physicists.

The course in Theoretical Mechanics, designed for the students of Quantum, Nuclear and Particle Physics, Bachelor’s degree, is the last theoretical summary of the experimental facts and the accumulated knowledge of the students of classical (non-quantum) mechanics from the secondary school and the general physics course. The course introduces in turn consistently enough the fundamentals and apparatuses of Newtonian mechanics, Lagrangian formalism, as well as the (canonical) Hamiltonian formalism of classical mechanics and the corresponding variational principles. Particular attention is paid to the relationship between the laws of conservation of mechanical quantities and symmetries. The theoretical material is illustrated with numerous concrete physical examples considered at the required theoretical and mathematical level. The main idea of the course is to follow the clear relations with the experimental foundations of mechanics to the most modern level and to point out the exact physical scope of applicability of classical mechanics as a model of physical reality.

The course “Optics” is the fourth part of the course in General Physics. It is a natural continuation of the course “Electricity and magnetism” (especially the topics concerning the electromagnetic waves). It also prepares the students for the next courses “Quantum physics” and “Interaction of the light with the matter”. The course is based on the knowledge of the students, acquired in other courses as “Mechanics”, “Thermodynamics and molecular physics”, and “Mathematical methods in physics”.
The content of the course includes the most important topics of the basic education in General physics, namely: geometrical optics and devices, propagation of the light in different media (depending on their electrical properties and symmetry); phenomena on the interface between two media; phenomena, concerning the wave nature of the light: interference and diffraction; devices, working using these phenomena; basics of spectral analysis; light devices and detectors as well an introduction to the basic quantum properties of the light, necessary for understanding of some optical phenomena as thermal radiation, photoelectric effect, radiation and absorption by real objects, lasers. In a separate chapter some basics of nonlinear optics are presented. The nonlinear polarization of a medium, nonlinear parametric effects and nonlinear correction of the refraction index are discussed. Seminars deepen and illustrate with appropriate problems the lectures. Demonstrations of the discussed phenomena are also included in the syllabus.
In the laboratory classes in optics, the basic optical phenomena are demonstrated and studied experimentally:
• Interference (Reilly’s interferometer and Newtonian rings seen through Desen’s device)
• Diffraction (diffraction grating, optical laser measurements, etc.)
• Dispersion (refraction of light through prism, Monochromator)
• Heat radiation (Heated body radiation)
The basic laws applicable to the different optics sections are studied experimentally :
• Wave optics (polarization of light, rotation of the polarization plane of light)
• Quantum optics (External Photo Effect)
• Geometric optics (Determination of focal lengths of lenses and lens systems).
Different optical constants, their spectral dependencies, and some dispersion characteristics (Absorption photometry, Abbe refractometer) are measured. Students are also acquainted with the measurement of the basic photometric quantities characterizing the optical radiation using the effect on the radiation receivers (Photometry) and the methods of measurement and quantitative characterization of color and color differences (Colorimetry). The first exercise is introductory. Its aim is to give students an overview of the laboratory classes and to familiarize themselves with the order of the lab and the safety rules in it.
Of the 16 laboratory exercises at the Faculty of Physics at the Optics Training Labs (at the Department of Condensed Matter Physics), an individual cycle of 12 exercises is accomplished by the students. The colloquium is held during the last week of the semester. With the experimental data obtained, a protocol is formed that includes appropriate mathematical and graphic processing.

The course covers the basics of computational physics and the algorithms, used to develop efficient tools for performing different mathematical operation. The calculations are presented from the numerical computation point of view, referring to their efficiency, algorithm bias and convergence. The topics include interpolation, integration, linear systems solving, eigenvectors and eigenvalues, differential equation solving, Monte Carlo methods and others.

This course for undergraduates (bachelor students) presents the general concepts and principles of the physics of atoms, molecules, and the interaction of ionizing radiation with matter. It represents how our knowledge about the microscopic structure of matter and radiation came about and which crucial experiments forced an extension and refinement of existing classical theories, culminating in the development of quantum theory, which is now accepted as the basic theory of atomic and molecular physics.

This course focuses on Classical Electrodynamics and Special Relativity. Students will learn the fundamental concepts and equations of electrodynamics, as well as the basics of special relativity. By the end of the course, students will be able to solve typical problems and have the necessary background to further develop their knowledge and skills in this subject area.

The course in Basic Quantum Mechanics is the third of four courses that make up the core of education in theoretical physics. This course introduces students to the basic principles of quantum mechanics and the basic methods and applications. This course provides the students with the necessary knowledge to solve quantum mechanical tasks and skills for qualitative and quantitative evaluation of physical phenomena in the microworld. The content of the course covers the necessary information for a future specialization in the field of theoretical physics and astrophysics, high-energy physics, atomic, molecular and optical physics and condensed matter physics.

The course aims to give a simple and up-to-data introduction to the physics of atomic nucleus. The major sub-topics in Nuclear physics, namely Nuclear structure, Nuclear decays and radioactivity, Nuclear reactions and Applications, comprise the main parts of the course. Within these main parts a broad selection of nuclear phenomena and characteristics are introduced and discussed as a special emphasis is made on the experimental roots of nuclear science. The course begins with the bulk properties of atomic nucleus and gradually moves towards more complex picture of the nucleus as a quantum mechanical many-body system which dynamics is primarily determined by the strong nuclear interaction but it is also affected by the Coulomb and the weak nuclear interaction. The properties of nuclear decays and reactions are also introduced and discussed not only as tools to study the atomic nucleus but also as phenomena which form the basis of the nuclear technology.

The topics span key areas of advanced quantum mechanics, beginning with time-dependent perturbation theory, which describes how quantum systems evolve under external influences using methods like variation of constants, Fermi’s golden rule for slowly varying fields, and Rabi oscillations in periodically driven two-level systems. The quasi-classical (WKB) approximation connects classical and quantum descriptions by analyzing particle behavior near turning points, enabling estimates of tunneling probabilities and energy quantization via the Bohr-Sommerfeld rule. The treatment of identical particles introduces symmetric and antisymmetric wave functions, distinguishing bosons from fermions, and explains phenomena like the Pauli exclusion principle, exchange interactions, and the electronic structure of atoms such as helium using the Hartree-Fock method. Finally, quantum scattering theory and relativistic quantum mechanics provide tools to study interactions and wave propagation, including the use of partial waves and the Born approximation for scattering, and relativistic formulations like the Klein-Gordon and Dirac equations, which account for particle-antiparticle dynamics and effects such as the Aharonov-Bohm phenomenon.

The subject of the course is the field of electronics applied to acquisition and processing of electrical signals generated by various types of radiation detectors. Basic principles and building blocks used for amplification, shaping, transmission, and analog-to-digital conversion of signals are studied. The students get acquainted with the techniques for amplitude and timing data acquisition. Among the included topics are: preliminary amplification of pulses by voltage and charge sensitive amplifiers, various means of pulse shaping, integrators, appropriate analog-to-digital conversion schemes, leading edge and constant fraction timing, time-to-amplitude conversion, single- and multi-channel analyzers, transmission lines, signal splitters, pulse counting, simulation of some electrical circuits with basic application, etc. In the laboratory the students assemble and investigate some relevant electronic circuits using analog, digital and mixed-signal integrated circuits and discreet components. Some pre-assembled modules are also used.

The aim of the course is to introduce to the students the Physics behind ionizing radiation detection and measurements. Different types of ionizing radiation detectors (solid state detectors, scintillation detector, gas-filled detectors, etc.) as well as their typical applications. The practical exercises straighten the students knowledge on the topics of the course and in addition teach them to work safely with various type of radiation sources and detectors. Some basic knowledge about the statistics and detector electronics is also introduced to the students.

 This course consists of two parts. In part Thermodynamics, the principles of thermodynamics, the method of the thermodynamic potentials, and the conditions for equilibrium of the thermodynamic states are presented. Several applications of the principles and the method of the thermodynamic potentials are considered. Part Statistical Physics encompasses classical and quantum statistical physics, as well as quantum statistics. The method of Gibbs and the principal distribution functions are presented. Several applications of Gibbs’ method are considered.

The course is an introduction to fundamental micro-objects (leptons, quarks, gluons, etc.) which, following given rules and laws of interaction, build nucleons, nuclei, atoms – microsystems better known by the students. The goal of the course is to familiarize the students with contemporary concepts about fundamental constituents of matter and their interactions. Basics of kinematics of elementary particles are presented. The symmetries of elementary particles (continuous and discrete, spatial and internal, global and local) and following conservation laws are discussed. The interactions are described with local (gauge) symmetry group formalism. Special attention is given to the experimental methods for study of elementary particles properties and their interactions, including present-day acceleration complexes and multi-detector systems for particle registration and identification. The emphasis is on the specifics of high-energy particles (~GeV), short lifetimes (~ns) and large background of particles. Basics of quark model and introduction to quantum chromodynamics, describing strong interaction, are shown. The experimental proofs for the existence of quarks and gluons are discussed. The weak interaction and Glashow-Weinberg-Salam model, describing electromagnetic and weak interactions, are presented. The neutrino mass problem and neutrino oscillations are discussed. The attempts for building theories, which unify electromagnetic, weak and strong interaction are presented. The main problems and trends of particle physics development are outlined.
The second part of the course are the seminars, which are devoted to solving problems. The problems are chosen in such a way that they complement, develop, and clarify lecture material. Successful problem solving does not need full use of mathematical methods in physics but rather depends on the level of understanding of physical ideas and orientation in the problem.
The third part of the course is doing laboratory work where the students will get to know basic detectors and research methods. They will have the opportunity to acquire, process and analyse data sets using modern computing systems. They will learn about scintillation and silicon detectors, will simulate detector systems and their response to high-energy particles.

The course Astrophysics is intended for undergraduate students in Quantum, Nuclear and Particle Physics. The program of the course aims to provide a systematic overview of main astrophysical topics, introducing students to the basics and the methodology of astrophysics, as well as the physical characteristics of various cosmic objects and environments.
The introductory classes are dedicated to the basic quantities, notions and laws used in different fields of astrophysics as well as fundamental parameters of cosmic objects. The program then focuses on stellar astrophysics: stellar atmospheres, spectra’ features, generation and transfer of energy in stars.
The properties of starforming regions are briefly discussed. Special attention is given to the condition fulfilled for starformation, protostellar and later evolution of stars, ending with the final stages of stars’ lifetime. A difference is made between low, intermediate and high mass stars.
Solar system and its components – planets, dwarf planets, asteroids, comets – are also considered. Also, a brief introduction to different methods for exoplanets search and analysis of exoplanets’ atmospheres is made.
The last topics in the program concerns galaxies in the Universe. Different galaxy types, their basic physical and observational properties, and fundamental relations are discussed.
The students are introduced to nearby galaxies, Local group of galaxies and large scale clustering.
The course is presented in accessible format and provides links to other fields of Physics.

In the section Dosimetry, basic dosimetry quantities and units are considered, as well as the physical principles of different methods for radiation measurements. Basic information in radiation biophysics is also provided. In the section “Radiation Protection” basic harmful effects of ionizing radiation are considered. A review of the contemporary knowledge of the radiation risk is made. On this basis the basic principle of Radiation Protection – “Risk vs. Benefit” is defined. The national radiation protection legislation is considered and also some key rules in case of radiation accident.

The course is devoted to the contemporary understanding of the basic constituents and their interactions. It covers extensively the Standard model of Particle physics which itself is based on the framework of the relativistic quantum mechanics and quantum field theory accompanied by the powerful formalism of the symmetries and group theory. Both global and local symmetries are covered together with the experimental data used to derive the relations within the Standard Model. While the topics are standard for any particle physics course (i.e. introductory or advanced) the difference is the depth of the presentation of the problems and their outcomes.

The course provides an introduction to the basic nuclear models used in describing the atomic nucleus within the framework of the variational principle. Special attention is given to encouraging the students to finding the connection between heavy theoretical expressions and a basic physics picture.

The aim of the course is to introduce the main contemporary methods of nuclear spectroscopy, the experimental set-ups, and the techniques for data manipulations used in nuclear physics experiments at low energies.
The course focuses on the interaction of the nuclear radiation with matter, the detectors for nuclear radiation and the related with them apparatus. The course includes the methods of γ-ray spectroscopy, α spectroscopy, β spectroscopy, nuclear lifetime measurements, and methods for construction of complex decay schemes.