Modern Physics I

Physics, First Cycle
Educational Physics
2 year
Hours per week – 1. semester:

Enrollment (completed exams in Physics I and II and Mathematics I and II).
Positive grade in Tutorials and completed homework are required to take the exam

Content (Syllabus outline)

Special theory of relativity:

Gallileo transformation and speed of light, Michelson and Morley experiment. Fundamental postulates of relativity. Lorentz transformation, space-time, time dilation and length contraction. Four-vectors, scalar product of four-vectors. Four-vectors of momentum, velocity and force. Momentum conservation. Systems of particles, collisions. Lorentz transformation of electric and magnetic field.

Quantum physics:

The problems in classical physics: stability of atoms, black body radiation, photoefect. Particles as waves, probability amplitude, wave function, indeterminacy principle. Physical quantities as operators. Schroedinger equation, eigenvalues and eigenstates of energy. Particle in infinite potential well, expansion in energy eigenstates. Harmonic oscillator. Dirac notation. Particle current density. Piecewise continuous potential, tunneling. Schroedinger equation in 3 dim. Particle in a box. Angular momentum: commutation rules, eigenvalues, spherical functions, rotator. Hydrogen atom: energy eigenvalues, eigenstates. Orbital magnetic moment, Stern-Gerlach experiment, spin. Two-level system. Angular momentum addition. Spin-orbit coupling. Zeeman effect. Radiative transitions, selection rules, width of spectral lines. Many electron atoms: single particle states, Pauli exclusion principle, periodic system. Visible and X-ray spectra. Energy levels of electrons in periodic potential, Kronig Penney model, concept of energy bands.

Chemical bonds: ionic bond, covalent bond, van der Walls bond. Molecular vibrations, rotations and spectra.


J. Strnad, Fizika, 3. del. DMFA, Ljubljana, 2002.
J. J. Brehm, W. J. Mullin, Introduction to the structure of matter. Wiley, 1989.
J. Berstein, P.M. Fishbane, S. Gasiorowitz, Modern Physics. Prentice Hall, 2000.
J. W. Rohlf, Modern Physics from a to Zo. Wiley, 1994.
K. Krane, Modern Physics. 2. ed. , Wiley, 1996.
T. Čopič, Zapiski in računalniške simulacij. Dostopno na spletu:

Objectives and competences

To acquaint with the basics of relativity theory and quantum physics as the basis for dealing with microscopic phenomena

Intended learning outcomes

Knowledge and understanding:

Knowledge and understanding of the indeterminacy principle, the meaning of the wave function, superposition, physical quantities as operators, eigenvalues and eigenstates of operators.


Solving simple quantum problems


Abstract modeling of physical systems

Transferable skills:

Basis for the understanding of microscopic phenomena: physics of atoms, molecules, nuclei, solid state

Learning and teaching methods

Lectures, seminars, individual consultations, probelm solving tutorials, homework.


2 written tests
Oral examination
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references
  1. VILFAN, Mojca, OSTERMAN, Natan, ČOPIČ, Martin, RAVNIK, Miha, ŽUMER,
    Slobodan, KOTAR, Jurij, BABIČ, Dušan, POBERAJ, Igor. Confinement effect on
    interparticle potential in nematic colloids. Phys. rev. lett. 101, 237801 (2008).
  2. GORJAN, Martin, MARINČEK, Marko, ČOPIČ, Martin. Pump absorption and
    temperature distribution in erbium-doped double-clad fluoride-glass fibres.
    Opt. express, 17, 19814(2009).
  3. PETELIN, Andrej, ČOPIČ, Martin. Observation of a soft mode of elastic
    instability in liquid crystal elastomers. Phys. rev. lett. 103, 077801 (2009).
  4. MERTELJ, Alenka, REŠETIČ, Andraž, GYERGYEK, Sašo, MAKOVEC, Darko,
    ČOPIČ, Martin. Anisotropic microrheological properties of chain-forming
    magnetic fluids. Soft matter 7, 118 (2011).
  5. MERTELJ, Alenka, CMOK, Luka, ČOPIČ, Martin, COOK, Gary, EVANS, Dean R.
    Critical behavior of director fluctuations in suspensions of ferroelectric
    nanoparticles in liquid crystals at the nematic to smectic-A phase transition.
    Phys. rev. E 85, 021705 (2012).