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# ZMF

**Course:** Fundamentals of Modern Physics

**Department/Abbreviation:** KEF/ZMF

**Year:** 2021

**Guarantee:** 'Mgr. Lukáš Richterek, Ph.D.'

**Annotation:** The course Fundamentals of Modern Physics consists of lectures and numerical exercises. Students will be acquainted with foundations of quantum and statistical physics, i.e. the disciplines that are necessary for understanding and explanation of phenomena solved by contemporary physics. The principles of the quantum physics and the examples of its applications will be presented. The attention will be paid to the context of classical and quantum physics, the quantum physics contribution in the description of physical

**Course review:**

1. Historical introduction. Old quantum theory of light, corpuscular-wave dualism, radiation. Planck's law, the photoelectric effect, the Compton effect. Bohr's theory of the structure of atoms . De Broglie waves, diffraction of electrons.
2. The concept of wave function, its physical meaning. Properties of wave functions. Representation of physical quantities, linear Hermitian operators, operator equations. Mean values ??of physical quantities. Operators of specific physical variables, commutation relations, the uncertainty principle.
3. Schrödinger equation, stationary and non-stationary states. Green's function. Limit transitions to classical mechanics. Rate of change of physical quantities, by the time derivative operator. Ehrenfest theorem. Parity condition.
4. Applications. Solutions for rectangular potentials, one-dimensional, three-dimensional potential well, the method of separation of variables. A potential barrier, the tunnel effect, cold emissions, a radioactive decay. One-dimensional and three-dimensional quantum linear harmonic oscillator (LHO). The particles in a spherically symmetric potential field. A model of the hydrogen atom, orbitals. Mechanical and magnetic orbital angular momentum of the electron.
5. Approximate methods of solving problems in quantum physics. The perturbation theory, variational methods. The stationary perturbation theory, non-degenerate and degenerate states, the non-stationary perturbation theory, the Fermi rule. Direct and general variational methods.
6. Free particles, Green's function of a free particle.
7. Representation theory. Wave functions and operators as vectors and matrices in a Hilbert space. Dirac notation. Coordinate, impulse and energy representations. Schroedinger's and Heisenberg's attitudes. The density matrix, pure and mixed states.
8. The spin of particles. its experimental discovery. Pauli spin matrices, the Hamiltonian of a particle in an electromagnetic field. The Pauli equation, basics of relativistic quantum mechanics. the Klein-Gordon-Fock equation, the Dirac equation.
9. Basic concepts of statistical physics. The phase space, the Liuoville theorem. Microcanonical , canonical and grand canonical ensembles. The statistical definition of entropy.
10. Statistical properties of the sum and the statistical integral, calculations of thermodynamic quantities, applications for some systems (Maxwell's distribution of velocities, monoatomic and diatomic ideal gases, the concept of paramagnetism).
11. Statistical distribution. fermions and bosons, Bose Einstein condensation.
12. A model of a photon gas and blackbody radiation.