Syllabus of lectures and exercises

Lecture syllabus

This syllabus is based on the lecture from 2019.

1. lecture: Harmonic oscillator including damped and excited case. Ordinary linear differential equations with real constant coefficients. The relationship between a complex and a real solution.
2. lecture: Approximation of small oscillations. Method of Modes. Normal coordinates.
3. lecture: Damped and excited small oscillations. A chain of atoms and its solution. Continuous limit.
4. lecture: Dispersion relation of a chain. The wave equation. Solving string motion with fixed ends by separation of variables. Initial value problem. Fourier series (without even and odd extension).
5. lecture: Fourier series - even and odd extensions. D'Alembert's solution to the wave equation. Initial value problem. Emission of (harmonic) travelling waves.
6. lecture: Continuous string - derivation of the wave equation. Longitudinal vs. transverse wave. Sound - wave equation for an ideal gas. Kinetic and potential energy density on a string.
7. lecture: Flow of energy on a string. Integral and differential conservation of energy. Energy in a travelling wave. General dispersion relation and phase velocity.
8. lecture: Reactive environment. Fourier transform. Quasi-monochromatic waves.
9. lecture: Wave packets. Relations of uncertainty. Group velocity.
10. lecture: Distortion of wave packets. Wave reflections. String termination. Connection of two strings.
11. lecture: Harmonic incident wave. Energy conditions. Frequency dependent transmission and reflection coefficients – case of massive connection. Transmission matrix.
12. lecture: Transmission matrix – connecting two strings for $z=L$. Waves in space – plane and spherical waves.
13. lecture: Electromagnetic planewave. Spectrum of electromagnetic waves.
14. lecture: Emission of electromagnetic waves. Radiation field.
15. lecture: Energy quantities in the EM field: energy density, energy flow, momentum density. Radiation pressure.
16. lecture: Power radiated by a moving charge – Larmor's formula. Refractive index of substance and plasma.
17. lecture: Waveguide – boundary conditions of perfect conductivity, modes, transparent and reactive medium. Description of polarization states.
18. lecture: Polarizer and wave plate. Polarization measurement.
19. lecture: Unpolarized light. Junction conditions of EM field at an interface of non-conductive media.
20. lecture: Fresnel formulas – the role of EM wave transmission and reflection at the interface of non-conducting media, the law of reflection and refraction, critical angle, transmission and reflection coefficients.
21. lecture: Fresnel forwmulas – completion, Brewster angle, polarization by reflection. Interference and influence of spatial and temporal coherence.
22. lecture: Diffraction – Babinet principle, Huygens-Fresnel principle, diffraction integral, Fraunhofer diffraction.
23. lecture: Young's experiment, diffraction grating, diffraction on a slit of finite width, angular beam divergence.
24. lecture: Effect of coherence on the diffraction pattern. Geometric optics – eikonal equation, local direction of propagation, rays as integral curves of local directions of propagation, Fermat's principle.
25. lecture: Photo effect, Compton scattering, blackbody radiation.
26. lecture: 2nd credit test

Exercises syllabus

This syllabus is based on exercises from 2019.

1. exercise: Mean values. Complex numbers and exponentials.
2. exercise: Longitudinal and transverse oscillator potential of the 1D case. Longitudinal oscillations of two weights on springs.
3. exercise: Transverse vibrations of two weights. Spring pendulum. Initial conditions. LC circuit.
4. exercise: Dispersion relation and modes of strings with fixed ends. Fourier series. Solving the initial value problem for a string.
5. exercise: Hammer and string. Superimposing of waves, beats, travelling and standing waves.
6. exercise: Test
7. exercise: Fourier transform, relations of uncertainty.
8. exercise: Dispersion relations, phase and group velocity. Telegraph equation.
9. exercise: Transmission and reflection coefficients when connecting two lines. Infinite reflections. Transmission matrix.
10. exercise: Spatial waves - travelling planewaves, dispersion relations. Superposition of travelling planewaves.
11. exercise: Completing spatial waves. Waveguide. Beginning of polarization 9.1-9.2.
12. exercise: Polarization
13. exercise: Interference and diffraction