**INHALTE**

# Lectures for the bachelor degree course of Technical Physics

### Experimental Physics 1

These lectures introduce the kinematics and dynamics of individual mass points. Newton's laws will be presented. The conservation of energy and momentum are central results. The Galilei transformation is used to describe motions in coordinate systems that move uniformly with respect to each other. Coordinate systems that are accelerated with respect to each other give rise to forces of inertia. The model of a point mass will be extended to systems of point masses with applications in the motion of planets. The chapter on rigid bodies culminates in the description of the dynamics of a spinning top by means of the Euler equations. The first part of Special Relativity is dediated to the Lorentz-Einstein transformation, time dilation and length contraction. The lectures close with the presentation of basic properties of solids, fluids and gases, the description of fluids in motion by the Navier-Stokes equation and straddles the first part of thermodynamics by the discussion of the kinetic theory of gases.

### Experimental Physics 2

Thermodynamics started in the course Experimental Physics 1 will be continued. The description of changes in thermodynamic states as well as the conduction of heat will be discussed. The laws of thermodynamics will be presented. Heat engines and their thermal efficiencies are treated. Oscillations and Waves represent the second part of the lectures where the driven, damped, harmonic oscillator plays an important role. The propagation of waves will be described analytically by the wave equation. Die Ausbreitung von Wellen wird analytisch mit der Wellengleichung beschrieben with a focus on sound waves. The lectures conclude with the second part of Special Relativity in which the relativistic Doppler effect will be used to explain the twin paradox.

### Experimental Physics 3

The lectures address electrostatics and magnetostatics. The Coulomb force and Gauss's law of electrostatics are central results of this part of the lectures. Magnetic fields of moving charges are described by Ampère's law and the Biot-Savart law. A highlight of the lectures is Faraday's discovery of the electromagnetic induction. A summary of all experimental findings is given by the Maxwell equations. In wave optics light propagation will first be described using the principles of Huygens and Fermat. Later, interference phenomena and their influence on the resolving power of optical instruments will be discussed. Temporal and spatial coherence are the main topics in this context. Birefrigence, wave plates, the laser and holography belong to the final topic of these lectures.

Problem class

Information on and access to the exercise series will be announced during the lectures.

Module

Experimental Physics 2a

### Experimental Physics 4

Lectures

Lecturer Prof. Dr. J. Kröger

The lectures intend to hone our conception of space, time and measurement. A brief introduction to the special relativity shows that the Galilei transformation known from Newtonian mechanics has to be replaced by the Lorentz-Einstein transformation. From these tranformations length contraction, time dilation and the equivalence of mass and energy will be inferred. The main part of the lectures addresses physics of particles at the ultimate size limit. After the discussion of the wave-particle duality, classical atom physics will lay the foundations for the subsequent quantum mechanical description of atoms, molecules and nuclei. Highlights are the Bohr atomic model, the Schrödinger equation and the Heisenberg uncertainty relations. Radioactivity and elementary particles conclude the lectures. Problem class Information on and access to the exercise series will be announced during the lectures.

Module

Experimental Physics 2b

### Solid State Physics 1

**Lectures**

Lecturer Prof. Dr. J. Kröger

Solid State Physics 1

The lectures intend to lay the foundations for modern solid state physics. First, the interaction between atoms and the classification of crystal structures will be discussed. Diffraction methods for structural analysis motivate the notion of the reciprocal lattice, the Ewald construction, the structure and the atomic form factor. The students will then be confronted with the dispersion relation of acoustic and optical phonons. The Einstein and Debye model belong to important results of this part of the lectures. Anharmonic effects will be introduced on the basis of thermal expansion and heat conduction. The electronic structure of solids represents another focus of these lectures. The Drude model of a classical electron gas serves as a starting point to describe the Wiedemann-Franz law and the Hall effect. Subsequently, the Sommerfeld model takes the Pauli principle into account and treats the electrons as a fermion gas. In the Bloch model the nearly free electron gas interacts with the ions via a periodic lattice potential. We will then deal with the motion of an electron gas in an external magnetic field.

The resulting Landau levels will help to understand the de Haas - van Alphen oscillations.

Semiconductor physics covers direct, indirect, intrinsic and doped semiconductors. In addition,

interfaces between semiconductors and the Schottky contact will be addressed. The dielectric

properties of solids conclude the lectures. The dielectric function will be elaborated and applied to the dispersion of plasmons, phonons, plasmon polaritons and phonon polaritons.

Problem classInformation on and access to the exercise series will be announcedduring the lectures.

**Modules**

Technical Physics 1 (TPh), Physical Optics (OTR, until academic regulations of 2008)

### Techniques of surface physics

**Lectures**

**Lecturer Prof. Dr. J. Kröger**

The lectures intend to lay the foundations for modern solid state physics. First, the interaction between atoms and the classification of crystal structures will be discussed. Diffraction methods for structural analysis motivate the notion of the reciprocal lattice, the Ewald construction, the structure and the atomic form factor. The students will then be confronted with the dispersion relation of acoustic and optical phonons. The Einstein and Debye model belong to important results of this part of the lectures.

Anharmonic effects will be introduced on the basis of thermal expansion and heat conduction. The electronic structure of solids represents another focus of these lectures. The Drude model of a classical electron gas serves as a starting point to describe the Wiedemann-Franz law and the Hall effect. Subsequently, the Sommerfeld model takes the Pauli principle into account and treats the electrons as a fermion gas. In the Bloch model the nearly free electron gas interacts with the ions via a periodic lattice potential. We will then deal with the motion of an electron gas in an external magnetic field. The resulting Landau levels will help to understand the de Haas - van Alphen oscillations. Semiconductor physics covers direct, indirect, intrinsic and doped semiconductors. In addition, interfaces between semiconductors and the Schottky contact will be addressed. The dielectric properties of solids conclude the lectures. The dielectric function will be elaborated and applied to the dispersion of plasmons, phonons, plasmon polaritons and phonon polaritons.

**Problem class**

Information on and access to the exercise series will be announced

during the lectures.

**Modules**

Technical Physics 2

# Lectures / Seminars for the master degree course of Technical Physics

### Solid State Physics 2

**Lectures**

Lecturer Prof. Dr. J. Kröger

Collective phenomena of the electronic system are key to these advanced lectures. In the first lectures screening of charges by the nearly free electron gas will be considered. To this end the dielectric function is evaluated in the approximations by Thomas and Fermi and by Lindhard. Screening leaves its footprints on the phonon dispersion, on the metal-to-insulator transition and is at the base of Landau's concept of quasiparticles. Subsequently, magnetism and superconductivity will be addressed. As a central result the microscopic origin to diamagnetism, paramagnetism and ferromagnetism will be unveiled. In particular band ferromagnetism will be described within the model put forward by Stoner and Wohlfarth. Magnetic domains and domain walls are most appropriate to introduce the concept of magnetic anisotropy energy. Magnetic excitations such as magnons, the Kondo and the Rashhba effect conclude the magnetism part of the lectures. The phenomenological description of superconductivity by the London equations is soon followed by its microscopic explanation due to Bardeen, Cooper and Schrieffer. The counterintuitive mutual attraction of two electrons to form a Cooper pair will be traced to the exchange of virtual phonons. The quasiparticle density of states of a conventional superconductor will be derived and corroborated by experiments. Magnetic flux quantization and the Josephson effect are the basis for the superconducting quantum interference device (SQUID), which represents a probe for extremely low magnetic fields. Type 2 superconductors, hight-temperature superconductors and novel superconducting materials conclude the lectures.

**Problem class**

Information on and access to the exercise series will be announced during the lectures.

**Modules**

Applied and experimental physics

### Physics of structures at the nanometer scale

**Lecture**

Lecturer: Prof. Dr. J. Kröger

"Small is different." This claim will be corroborated by the peculiar physical properties of structures at the nanometer scale. Apart from fabrication techniques the lectures prioritize the analysis of structural, electronic and magnetic properties of small assemblies ranging from clusters down to single molecules and atoms. The quantized charge transport through conductors on the atomic scale conclude the lectures.

**Problem class**

Information on and access to the exercise series will be announced during the lectures.

**Modules**

Applied and experimental physics

### Surface and interface physics

**Lectures**

Lecturer Prof. Dr. J. Kröger

Complementary to the preparatory lectures on "Techniques of surface physics" the emphasis here is on generaly concepts rather than on experimental methods. Relaxations and reconstructions of surfaces will demonstrate the impact of a surface on atom positions of a solid. Electronic states of clean surfaces, the binding of adsorbates to surface sites as well as vibrational properties will be addressed. Regarding applied sciences magnetism at surfaces plays an important role. Diffusion, nucleation and growth conclude the lectures. Knowledge of solid state physics is helpful for understanding the presented topics.

**Problem class**

Information on and access to the exercise series will be announced during the lectures.

**Modules**

Surface and interface physics

### Seminar: Physics of surfaces and interfaces

**Seminar**

Lecturer Prof. Dr. J. Kröger

The seminar offers the opportunity to study special topics of modern surface physics in more detail. Current research activities, experimental techniques as well as chapters of the accompanying lectures on surface and interface physics serve as a rich pool for presentations at the** **graduate level. Apart from professional training the student will acquire helpful presentation techniques.

Information on the seminar will be disseminated in the first lectures on scanning probe methods.

**Modul**

Surface and interface physics

### Scanning probe methods

**Lectures**

Lecturer Prof. Dr. J. Kröger

The scanning tunneling microscope has revolutionized our picture of processes on the atomic length scale. The lectures will preponderantly address experimental aspects of scanning tunneling microscopy, spectroscopy and atomic force microscopy. First, experimental requirements for the operation of a scanning tunneling microscope will be discussed. Subsequently, different imaging modes and spectroscopy methods shall be introduced. Some emphasis is given to inelastic and spin-resolved scanning tunneling spectroscopy. The lectures strive for conveying the basics of scanning probe methods as well as for presenting results of current research.

**Modules**

Surface and interface physics