Physics of Materials

Course Description

From Classical to Quantum Mechanics. Introduction to Quantum Mechanics, Solution of the Schrodinger Equation, Particle in One-dimensional Square Walls, Infinite Potential Barriers. Electronic Orbitals. Quantum Harmonic Oscillator. Classical and Quantum Statistics: Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein Distribution. Free and quasi-free electronic gas, Theory of Phonons. The Band Theory. Brillouin Zones. Quantum Theory of Semiconductor Structures. Electronic Properties of Dielectrics. Quantum-Mechanical Description of Polarization. Magnetic Properties of Materials, Diamagnetism, Para magnetism, Ferromagnetism. Low Temperatures Superconductivity. BCS Theory. Josephson?s Effect. SQUIDs and LTS. Fiber Optics. Nuclear Magnetic Resonance. Medical and Technical Applications. Synchrotron Radiation. Basics of Nano-Physics.

General Competencies

Education is focused on the deep understanding of Quantum Physics concepts and methods, and modern nanotechnology knowledge and techniques. Students will be educated in basic knowledge of describing and understanding of modern materials in Electrical Engineering, Information Technology and Computer Science. An emphasis will be also given on the practical skills to analyze as well as to simulate by the advanced programming tools the problems in the related topics (miniaturization, quantum computers, parallelization, and innovative materials).

Learning Outcomes

  1. Describe simple quantum systems.
  2. Apply quantum mechanics to elementary processes.
  3. Derive solutions for the hydrogen atom.
  4. Apply classical and quantum distributions.
  5. Relate classical and quantum description on the thermal properties.
  6. Analyze potentials and conductivities in crystall lattice.
  7. Explain fermion pairing in BCS theory.
  8. Analyze electric ana magnetic properties in technology.

Forms of Teaching


Lectures with AV support. Scientific movies on related contemporary research. Simple experiments and demonstrations.


Examples and problem solutions.


Regular - weekly consultations.


Individual presentations of special topics.

Acquisition of Skills

Work on computer and knowledge in simulations, data handling, and searching on articles and solutions in quantum physics.

Grading Method

By decision of the Faculty Council, in the academic year 2019/2020. the midterm exams are cancelled and the points assigned to that component are transferred to the final exam, unless the teachers have reassigned the points and the grading components differently. See the news for each course for information on knowledge rating.
Continuous Assessment Exam
Type Threshold Percent of Grade Threshold Percent of Grade
Homeworks 0 % 10 % 0 % 10 %
Class participation 0 % 10 % 0 % 10 %
Mid Term Exam: Written 0 % 40 % 0 %
Final Exam: Written 0 % 40 %
Exam: Written 0 % 40 %
Exam: Oral 40 %

Week by Week Schedule

  1. Basics of quantum physics. Relativistic equations of matter waves. Schroedinger equation.
  2. Heisenberg's uncertainty principle. Transmission and reflection on potential step.
  3. Tunnel effect. WBK approximation.
  4. Electron states in a potential well. Field emission. Contact potential.
  5. Hydrogen atom.
  6. Pauli's exclusion principle. Quantum mechanical harmonic oscillator.
  7. Statistical distributions: Fermi-Dirac, Bose-Einstein.
  8. EXAM
  9. Thermal properties of materials. Einstein and Debye model.
  10. Kronig-Penney model of potential lattice. Brillouin zones. Effective electron and hole mass.
  11. Conductivity. Semiconductor conductivity. Semiconductor applications.
  12. Superconductivity. BCS theory. Josephson effect and applications. LTS technology. HTS materials.
  13. Electrical properties of materials. Polarization. Dielectric permittivity. Optical fibers.
  14. Diamagnetism. Paramagnetism. Ferromagnetism. NMR and applications in physics of materials.
  15. EXAM

Study Programmes

University graduate
Computer Engineering (profile)
Mathematics and Science (2. semester)
Computer Science (profile)
Mathematics and Science (2. semester)
Control Engineering and Automation (profile)
Mathematics and Science (2. semester)
Electrical Engineering Systems and Technologies (profile)
Mathematics and Science (2. semester)
Electrical Power Engineering (profile)
Mathematics and Science (2. semester)
Electronic and Computer Engineering (profile)
Mathematics and Science (2. semester)
Electronics (profile)
Mathematics and Science (2. semester)
Information Processing (profile)
Mathematics and Science (2. semester)
Software Engineering and Information Systems (profile)
Mathematics and Science (2. semester)
Telecommunication and Informatics (profile)
Mathematics and Science (2. semester)
Wireless Technologies (profile)
Mathematics and Science (2. semester)


M. Baće, L. Bistričić, V. Borjanović, D. Horvat, T. Petković (2011.), Riješeni primjeri i zadaci iz fizike materijala, recenzirani udžbenik, Hinus, Zagreb
V. Knapp i P. Colić (1997.), Uvod u električna i magnetska svojstva materijala, Školska knjiga, 2. izd., Zagreb
H. M. Rosenbeerg (1989.), The Solid State. An introduction to the physics of solids for students of physics, material science, and engineering, 3rd ed., Oxford University Press, Oxford
Edward L. Wolf (2006.), Nanophysics and Nanotechnology: An Introduction to Modern Concepts in Nanoscience, Wiley–VCH Verlag GmbH&Co. KGaA, Weinheim, 2nd ed.
S. Blundell (2009.), SUPERCONDUCTIVITY: A Very Short Introduction, Oxford University Press, Oxford
(.), Uvod u fiziku čvrstog stanja V. Šips Školska knjiga, Zagreb 1991,
(.), Modern Physics J. W. Rohlf J. Wiley & Sons, New York 1994,
(.), Quantum Mechanics for Applied Phyisc and Engineering A. T. Fromhold, Jr. Academic Press, New York 1981,

Associate Lecturers


ID 34565
  Summer semester
L3 English Level
L1 e-Learning
45 Lectures
0 Exercises
0 Laboratory exercises
0 Project laboratory

Grading System

85 Excellent
75 Very Good
60 Good
50 Acceptable