Physics of Materials

Data is displayed for academic year: 2023./2024.

Course Description

Transition from classical to quantum-mechanical description of matter. Wave equation in three dimensions. Solutions, properties, interpretations, and quantum numbers set with possible values. Approximative methods of quantum mechanics: WBK approximation and applications. Perturbation theory of QM and applications. Applications of quantum distributions on bosonic and fermionic systems. Density of states and partition functions. Bose–Einstein condensates (superconductivity, quantum computers). Quantum mechanics and periodic potential (lattice): conductivity of electrons and holes, drift velocities, relaxation times, mobility. Langevin function: applications. Lorentz field and Clausius–Mossotti formula. Quantum theory of magnetism: magnetic moments related to Schrödinger equation. Electron spin and Landé factor. Hund’s rules and applications. Spintronics and applications (quantum computers). NMR and applications (quantum computers). Superconductivity at low temperatures: Meissner effect, London equations and penetration depth. Cooper pairs and BCS theory. Magnetic flux quantization (fluxon) and quantum metrology. Superconductivity at high temperatures. Phenomenology of crystal superconducting heterostructures. Quantum Hall effect. Applications of HTS materials for technology (quantum dots, thin films, magnets).

Study Programmes

University undergraduate
[FER3-EN] Computing - study
Elective Courses (6. semester)
[FER3-EN] Electrical Engineering and Information Technology - study
Elective Courses (6. semester)

Learning Outcomes

  1. Describe basic concepts of quantum-mechanical pictures of matter.
  2. Apply approximative methods of quantum mechanics into desription of matter.
  3. Derive wave equation in three dimensions.
  4. Apply classical and quantum distributions.
  5. Analyze potentials and conductivity in crystall latice.
  6. Explain fermion pairing in BCS theory at low temperatures.
  7. Describe quantum theory of magnetism and its application in quantum metrology and quantum computers.
  8. Analyze electric and magnetic properties of materials in technology.

Forms of Teaching


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

Seminars and workshops

Individual presentations of special topics.


Examples and problem solutions.

Independent assignments

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


Attending lectures (P), solving examples and excercises (V) laboratory excercises (L) on lectures. Individual and/or group presentations of specific topics - seminars (S)

Grading Method

Continuous Assessment Exam
Type Threshold Percent of Grade Threshold Percent of Grade
Homeworks 0 % 10 % 0 % 0 %
Class participation 0 % 10 % 0 % 0 %
Mid Term Exam: Written 0 % 40 % 0 %
Final Exam: Written 0 % 40 %
Exam: Written 0 % 40 %
Exam: Oral 40 %

Week by Week Schedule

  1. Structure of matter at microscopic level. Crystal structure. Bragg law. Crystal lattices. Crystal symmetry.
  2. Schrödinger equation and specific potentials: infinite and finite potential well. Harmonic oscillator. Delta-function potential. Spherical potential well. Postulates of quantum mechanics.
  3. Schrödinger equation in 3 dimensions. Angular momentum. Solution for hydrogen atom. Quantum numbers. Pauli principle. Mathematical formalism of quantum mechanics.
  4. Continuity equation. Uncertainty relations. Potential step. Tunnel effect. WBK approximation. Field emission. Alpha decay.
  5. Atom and molecular bonding. Effective potentials. Ionic, covalent, metal and van der Waals bonds. Madelung constant.
  6. Classical and quantum statistical physics. Distribution and partition functions, density of states. Maxwell-Boltzmann distribution.
  7. Free electron gas. Fermi-Dirac distribution. Fermi energy, temperature, velocity and wave vector. Bose-Einstein distribution. Bose-Einstein condensation.
  8. Midterm exam
  9. Heat capacity of materials. Dulong-Petit law. Einstein crystal model. Debye crystal model. Heat expansion and heat conduction: classical and quantum approach.
  10. Dielectrics. Polarization mechanisms. Electric susceptibility. Lorentz field. Clausius-Mossotti relation. Polarization by orientation. Langevin function. Quantum-mechanical description of polarization.
  11. Dispersion of electromagnetic waves. Apsorption in dielectrics. Electric properties of conductors. Drude-Lorentz conduction theory. Free electron gas. Periodic potentials. Kronig-Penney model. Dirac comb.
  12. Energy bands. Brillouin zones. Effective mass. Density of states and carrier concentrations in conduction and valence bands. Electron mobility. Intrinsic semiconductors. Effective electron and hole concentrations. Fermi energy temperature dependence. Extrinsic semiconductors. Semiconductor elements.
  13. Magnetic properties of materials. Magnetic moment. Magnetic susceptibility. Diamagnetism. Electron spin. Pauli paramgnetism. Lande factor. Hundt rules. Ferromagnetism. Magnetic domains. Curie law. NMR.
  14. Superconductivity. Meissner effect. London equations. Penetration depth. Magnetic flux quantization. Cooper pairs. BCS theory of superconductivity. High temperature superconductivity.
  15. Final exam


(.), Baće M.; Bistričić, L.; Borjanović, V.; Horvat, D.; Petković, T. Riješeni primjeri iz fizike materijala, recenzirani udžbenik. Hinus, Zagreb, 2011.,
(.), Knapp, V; Colić, P. Uvod u električna i magnetska svojstva materijala, udžbenik. Školska knjiga, 2. izd. 1997.,
(.), 1. Rosenberg, H. M. The Solid State. An introduction to the Physics of solids for students of physics, material science, and engineering, 3rd ed., Oxford University Press, Oxford 1989.,
(.), 2. A. F. J. Levi, Applied quantum mechanics, Cambridge University Press, Cambridge, 2003.,
(.), 3. L. Susskind and A. Friedman. Quantum Mechanics The Theoretical Minimum, Basic books - Perseus Books Group. New York, 2014.,
(.), 4. E. L. Wolf, Nanophysics and Nanotechnology, Wiley – VCH Verlag GmbH & Co. KGaA, Weinheim, 2004.,
(.), 5. L.I. Schiff, QUANTUM MECHANICS, McGraw-Hill Book Company, 3rd edition, 1968.,

For students


ID 223349
  Summer semester
L1 English Level
L1 e-Learning
45 Lectures
0 Seminar
8 Exercises
5 Laboratory exercises
0 Project laboratory

Grading System

85 Excellent
75 Very Good
60 Good
50 Sufficient