Table of lessons, physics curriculum for Master's Dregree

	Semester	Experimental Physics	Theoretical Physics	Higher Mathematics	Subsidiary Subjects		Practicum (Lab Courses)	Hours per Week
	1 (30 cr)	I Mechanics, Thermo- dynamics (11 cr) 4/2/2*		Analysis I Algebra I (12 cr) 6/3/0	Computer Science I (5 cr) 2/2/0		Practicum in Physics I (2 cr) 2	21 + 2*
	2 (30 cr)	II Elektro- megnetism, Optics (11 cr) 4/2/2*		Analysis II Algebra II (12 cr) 6/3/0			Practicum in Physics II (7 cr) 4	19 + 2*
	3 (30 cr)	III Atomic and Molecular Physics (8 cr) 4/2/0	I Mechanics (8 cr) 4/2/0	Analysis III (7 cr) 4/2/0	Chemistry I (2 cr) 2/0/0		Practicum in Physics III (5 cr) 4	24
	4 (30 cr)	IV Nuclei and Elementary Particles (5 cr) 2/2/0	II Quantum Mechanics (8 cr) 4/2/0	Analysis IV (7 cr) 4/2/0	A: Chemistry II (2 cr) 2/0/0 B: Coputer Science II (5 cr) 2/2/0		Practicum in Physics IV (2 cr) 2 Practicum in Chemistry A: 4 / B: 2 (6 cr / 3 cr)	24
		First Examination
	5 (30 cr)	Physics of Condensed Mater II (7 cr) 3/1/0	III Electro- dynamics (11 cr) 4/2/0				Advanced Practicum I (6 cr) 6	20
	6 (30 cr)	Physics of Condensed Mater II (7 cr) 2/1/0	IV Statistics, Thermo- dynamics (11 cr) 4/2/0				Advanced Prakticum II (6 cr) 6	20
	7 (30 cr)	Atomes, Molecules, Lasers (5 cr) 2/1/0	V Continuum Physics (11 cr) 4/2/0				Laboratory Prakticum I Overview (8 cr) 6	18
	8 (30 cr)	Selected Topics from Modern Physics (4 cr) 2/0/0	VI Selected Topics from Theoretical Physics (8 cr) 4/0/0	Advanced Seminar (4 cr) 0/2/0			Laboratory Practikum II Specialization (12 cr) 6	14
		Final Examination
	9 10	Diplom Thesis (60 cr)
+/o/* : + = Lecture / o = Discussion section / * = group learning (tutorial) in place of required seminar course A: Chemistry elective / B: Computer Science elective ( _ cr): ECTS credit points

Distribution of semester credits:

Grundstudium (4 semesters)			120 cr
Hauptstudium (6 semester2)			180 cr
davon:
	– experimenta physics	23 cr
	– theoretical physics	41 cr
	– advanced seminar	4 cr
	– requirde elective in physics	10 cr
	– requirde elective in another area	10 cr
	– advanced laboratory practical	12 cr
	– laboratory practical	20 cr
	– diplom thesis	60 cr
Total			300 cr

B. Grundstudium, Fundamental Courses

Experimental Physics I: Mechanics and Thermodynamics

W	4/2/2*	11 cr

In this course students will be shown how experimental experience of a phenomenon leads to quantitative formulation of its underlying principles. This includes stating a scientific hypothesis, designing and performing an appropriate experiment to test the hypothesis, analyzing the results, and developing a mathematical expression and generalization for them.
Specific topics that are covered are the kinematics and dynamics of a point mass, two-body motion, mechanical vibrations and waves, rigid bodies, non-rigid bodies, thermodynamics, and gas kinetics.
Particular emphasis is placed on the principles and methods which occur repeatedly in solutions of physical problems, for example, Newton's equations of motion, the expression for a harmonic oscillator, equations of motion for bodies in a collision, and also the steps of approximation in the development of a physical model: point mass, rigid body, continuum, thermodynamic (phenomenological) and statistical descriptions, the laws of thermodynamics. Applications to astro-, geo-, and particle physics, as well as to chemical and thermal technologies (Wärmetechnik) are also discussed.
Problem sets and quizzes are offered in the accompanying discussion sections. Small study groups ("Arbeitsgemeinschaften") can be organized for students to perform further exercises on the physical and mathematical principles discussed in the lecture.

Experimental Physics II: Electromagnetism and Optics

S	4/2/2*	11 cr

As in Experimental Physics I, the structure of this course follows the path taken between experimental experience and quantitative formulations of fundamental laws, here, of electromagnetism and optics. Specifically, the lectures cover electrostatics, stationary currents, magnetism, time-dependent fields, time-dependent currents, electromagnetic oscillations and waves, geometrical optics, wave optics, and optical instruments.
As in the first course, special emphasis is placed on the general methods and principles which appear in many physical problems, for example, the definition and description of a field, analogies and differences between electric and magnetic fields, long solenoids and plate capacitors, Maxwell's equations, the description of waves, and typical wave phenomena. During the course, students will be guided toward the "interface" of theoretical description and real applications in electrical devices, electronics, optical devices and lasers.
In addition to the usual tutorial discussions, small study groups can be organized to allow students to deepen their understanding of physical and mathematical aspects of the material.

Experimental Physics III: Atomic and Molecular Physics

W	4/2	8 cr

What is an atom and how big is it? Is it possible to see individual atoms? Are electrons and photons wave- or particle-like? What is the structure of an atom and how are molecules, clusters, and solids formed from atoms? In these lectures these questions will be answered with the discoveries of historically important, but also state-of-the-art experiments. We will discuss scattering experiments; the interaction of atoms and molecules with light of various wavelengths; and the behavior of atoms and molecules in electric and magnetic fields. Students may get the impression that this is merely a summary of observations of various experiments. Indeed, it is not very easy to understand atomic and molecular physics without an understanding of quantum mechanics. Nevertheless, it an important goal of this course for students to be able to systematically interpret the observations of the presented experiments and thus be led to the seminal results that will be treated again in the fourth semester, in theoretical physics, on a formal mathematical basis. A not less important objective is for students to become familiar with the modern experimental methods and analytical approaches that led to the development of e.g., the laser or the tunneling microscope.

Key words and concepts: Atom, photon, free electron, characteristics of matter waves, hydrogen atom, basics of quantum mechanics, optical transitions, multi-electron systems, periodic table of the elements, atoms in electric and magnetic fields, structure of molecules, energy levels of diatomic molecules, clusters - from atoms to solids.

Experimental Physics IV: Nuclei and Elementary Particles

S	2/2	5 cr

What are exactly the fundamental building blocks of matter? What are atomic nuclei made of? What are hadrons, leptons, and quarks? What are the fundamental interactions between these particles and their anti-particles?
To answer these questions (as well as can be done with today's knowledge base), as in the course on atomic and molecular physics, in this course we will also present the results of historic experiments as well as the observations of current experiments in high-energy physics. But in addition to this fascinating, virgin realm of physics (fundamental forces of nature), in this course students will learn about nuclear stability, nuclear fission and fusion, radioactive decay, the interaction of alpha-, beta-, and gamma-radiation with matter, dosimetry, and radiation shielding. This course will cover nuclear magnetic resonance (nmr), the Mössbauer Effect, gamma-ray spectroscopy, and collisions between electrons and positrons.

Key words and concepts: Properties of nuclei, nuclear stability and decay, radioactivity, interaction of particles with matter, nuclear reactions, special experiments in nuclear physics, radiation shielding, nuclear power plants, nuclear structure, scattering experiments, production of subatomic particles, fundamental forces of nature, elementary particles.

Theoretical Physics I: Mechanics

W	4/2	8 cr

Motion of a particle

• Fundamental expressions of space, time; relativity principle; Galilei and Lorentz transformations; Newton's equations of motion, the integrability problem
• Motion in one dimension
  Velocity dependent forces, space-dependent force and definition of a potential, free fall, harmonic oscillator, frictional force, damped oscillator with and without a harmonic driving force, Green's functions
• Vectorial representation of motion
  Representation of curves and surfaces, motion of a point through space, isotropic oscillator, trajectory of a projectile with friction, rotational motion, charge in a homogeneous magnetic field
• Conservation laws
  Conserved quantities, conservation of momentum, conservation of angular momentum, conservation of energy, force as a potential gradient
• Motion in a central field
  Polar coordinates, combination of the laws of conservation of angular momentum and energy, bound states, planetary motion

Systems of particles

• Two-particle system
  Equation of motion and interaction, conservation laws, separation of center-of-mass and relative motions, elastic collisions
• Many-particle system
  conservation laws, pair-wise interactions, transition to continuum

Advanced Mechanics

• Variational principle
  Variation of trajectories, Lagrange functions of simple systems
• Phase space and the Hamiltonian description
  Expression of motion in phase space, Hamiltonians, canonical equations, time dependence, conserved quantities, Poisson brackets, and transition to quantum mechanics

Theoretical Physics II: Quantum Mechanics

S	4/2	8 cr

This course presents the fundamental theoretical concepts required for the description of microphysical phenomena. We begin by presenting experimental results which cannot be explained by classical mechanics alone and proceed, step-by-step, toward devising the mathematical apparatus of quantum mechanics. A major portion of the class is devoted to the application of the Schrödinger equation to simple quantum systems (locally constant potential, harmonic oscillator, hydrogen atom). Spin is discussed in the context of the non-relativistic Pauli equation. Systems for which solution via the Schrödinger equation is difficult, for example, multiple particle systems and collision processes, will be treated by various approximation methods, e.g., the variational principle and perturbation theory. Students will learn that these methods are the basis for attempting solutions of more complex problems, requiring more theoretical sophistication.

Key words and concepts: Mathematical and physical fundamentals, Schrödinger equation, mathematical apparatus of quantum mechanics, central field, spin, approximation methods, many-particle systems, quantum theory of scattering.

Practicum in Physics I - IV

W / S / W / S	12	16 cr

In the practicum, students learn to plan, construct, execute, and evaluate experiments. Basic measurement and analysis procedures are learned, and first-hand experience of physical laws and phenomena is gained, from selected laboratory exercises in mechanics, thermodynamics, optics, electromagnetism, and atomic and molecular physics. Students should be able to deepen their understanding of physics and of cause-and-effect relationships in physical processes.
Students are trained to work independently, maintain an exact laboratory record, and to critically evaluate their measurements. They learn the basic ways of error analysis. To pass the course and obtain a certificate "Physikalisches Grundpraktikum", 38 experiments must be completed.

C. Hauptstudium, Advanced Courses

Physics of Condensed Matter I

W	3/1	7 cr

In this course the properties of crystalline solids are described via the model of an infinite crystal. In the adiabatic approximation the slow movement of the atoms is separated from the fast motion of the electrons, thus allowing a sequential treatment of the vibronic, electronic, and finally the optical, magnetic, and superconducting properties of solids. The course concludes with a discussion of effects which appear for spatially limited solids, e.g., quantum wells, wires, and dots.
The discussion section will be primarily concerned with providing students with a feeling for the dimensions of parameters typical for solids, for example, the bandgap energy of semiconductors in relation to the thermal energy kT. This is of extreme importance when estimating the probability of observing a physical effect under given experimental conditions.

Physics of Condensed Matter II

S	3/1	7 cr

This course focuses on spectroscopic methods of characterizing solids, in particular, their surfaces. Methods of sample preparation in ultra-high vacuum and sample growing methods, specifically, epitaxy, are introduced. Various probes, e.g., electrons, heavy-particle beams, light, and their interactions with solids are discussed, and the various information provided by each probing method are compared. Electron spectroscopic methods, such as Auger and photoemission spectroscopy, and optical methods, such as infrared and Raman, are presented along with electrical measurements. A summary of the newest developments in scanning probe methods concludes the course.
In the discussion section the research apparatuses used at the Institute of Physics will be demonstrated.

Atoms, Molecules, Lasers

W	2/1	5 cr

Atoms

Electronic structure, selection rules, eigenvalues, hydrogen atoms, Schrödinger equation

Molecules

Chemical bonds, hydrogen molecule, (Hund-Mullikan variational approximation, Heitler-London), Born-Oppenheimer approximation, Franck-Condon principle, vibrational states, rotational states, reaction dynamics, magnetic properties

Interaction between radiation and matter

Linear response, nonlinear properties

Laser/Maser

Principle of operation (population inversion, rate equations, coherence), gas laser, solid state laser, dye laser

Modern spectroscopic methods

Coherent methods, saturation spectroscopy, laser cooling of atoms, magnetic resonance experiments, level-crossing experiments, molecular beams, cluster beams, wave packet dynamics, fluorescence correlation

Selected Topics from Modern Physics

S	2/0	4 cr

This series of lectures discusses current problems in solid state physics on a microscopic level. Primarily metallic systems are discussed, however, some emphasis is placed on the metal-insulator transition. Subsystems such as the static structure, the electronic system, dynamic structure, and the connection and interaction between energy and momentum are presented. Typical changes that occur in the transition from a disordered to a quasi-crystalline and single crystalline solid are treated.

Theoretical Physics III: Electrodynamics

W	4/2	11 cr

Electrostatic field:

Sources = charges; fields of highly symmetric charge distributions; electrostatic potential; multipole expansion; Poisson equation; image charges; theory of potentials

Fields of inductance of stationary currents:

Vortices = currents; current density and conservation of charge; Biot-Savart Law; vector potentials

Dipoles and dipole layers:

electrical and magnetic dipole moment; potentials and fields; torque and force in external fields; Larmor precession

Static fields in a medium:

microscopic and macroscopic charges; currents and fields; oriented and induced atomic dipoles; fields (E, D, P) and (B, H, M); material equations; boundary problems; magnetostatics

Maxwell equations:

Induction law and Lenz' law; electromotive force and frame of reference; self inductance and mutual inductance; displacement current; Viererpotential; gauge conditions; delayed potentials

Energy and momentum:

field energy (self and interaction); the relation between potential energy and force; energy density and energy flow density; Lorentz force; momentum density and the Maxwell tensor; interaction between current loops

Time-dependent electromagnetic fields:

slowly moving charges; skin effect; wave equation and the Telegrafengleichung; phase velocity; index of refraction; plane waves; spherical waves; electric dipole radiation (far-field and near-field); radiation pressure

Applications and mathematical tools:

derivation of the field distribution from given charge, current, and material distributions; energy and force; wave dynamics and scattering; vector potentials, sources, and vortices; line integrals, surface integrals, volume integrals, integral theorems; Green's functions, partial differential equations; spherical harmonics, cylindrical harmonics

Theoretical Physics IV: Statistics and Thermodynamics

S	4/2	11 cr

Thermodynamical description:

Equilibrium, state variables, intensive variables, equations of state, model systems

The Laws of Thermodynamics:

the internal energy state variable, heat capacity, irreversibility, cyclic processes, the entropy state variable, temperature, Clausius inequality, entropy near T = 0

Theoretical Physics V: Continuum Physics

W	4/2	11 cr

This course is an introduction to modern methods of describing non-rigid media using field theory, and the fundamentals of the theory of elasticity and hydrodynamics. The course introduces kinematic tensors such as for deformation and velocity gradients, and Cauchy's tensor for the shear modulus. Important theoretical models for elongation, shear, torsion, and bending are discussed in their linearized approximations (geometrical and physical linearization). In a treatment of hydrodynamics we deal with the equations of motion for ideal and viscous fluids, from which the fundamental laws of fluid dynamics are derived, such as those governing vortices and simple flow geometries. Advanced topics such as properties of nonlinear materials and stability theory (critical point phenomena, turbulence) will also be touched upon.

Keywords: Kinematics of deformable bodies, kinetics, theory of elasticity, hydrodynamics.

Theoretical Physics VI: Selected Topics from Modern Physics

S	4/0	8 cr

Thermal radiation

Radiation field and photons

Photon statistics

Calculation of thermodynamic state variables

Density of states and spectral distribution

Quantum statistical description of time-dependent states

The statistical operator and the von-Neumann equation

Pure and mixed states

State evolution in closed systems

Time-dependence of average values and entropy

Relaxation processes in macroscopic systems

Quantum mechanical calculation of transition rates (golden rule)

Energy exchange via external perturbations

Energy conservation in internal perturbations, nonradiative processes

The master equation and irreversibility

Relaxing subsystem in a heat bath

Relaxation of two- and more-level systems

Electron-photon interactions

Interactions of charged particles with electromagnetic fields

Lagrange function of a radiation field and the Hamilton formalism

Eigenvibrations and photon counts

Induced emission and absorption processes

Quantization of a radiation field, photon states and oscillator methods

Rates of spontaneous and induced processes

Dipole approximation, absorption cross sections, summation rules for oscillator strengths

Advanced Seminar

S	0/2	4 cr

The "Oberseminar" provides students with a chance to prepare and present a lecture on a subject of their choice, in the areas of solid state physics and materials science. The talk should be a report on both the theoretical and experimental state-of-art. Students can choose among: fullerenes and fullerides, Landauer-Büttiker theory, spin glasses, the glass transition, bulk metallic glasses nanocrystalls, fractals, relaxations.

Physics Elective

W + S	6	10 cr

Usually the elective course in physics is held over two semesters. The total number of semester hours is flexible, and can be distributed among lecture and discussion sections. Each year, four different electives are offered. The topics of each elective are chosen by each faculty member and are mentioned in Section III C.

Non-Physics Elective

W + S	6 (8)	10 cr

The non-physics electives are taught by the Institute of Chemistry and other departments. These course span typically two semesters; a distribution of credit hours among lectures and discussion sections is possible. Courses are offered in

• Economics
• Computer Science
• Chemistry/Physical Chemistry
• Mathematics
• Technical Thermodynamics (Chemical Engineering?)
• Fluid Mechanics
• Telecommunications technology/Microengineering
• Electronics/Microelectronics

Advanced Practicum I and II

W + S	12	12 cr

In addition to gaining a familiarity with various areas of physics, the Advanced Practicum is intended to introduce students to day-to-day laboratory work which requires developing an ability to grasp, on short notice, new techniques and topics in physics, keeping an accurate record of the procedures and experiments undertaken, critical analysis of the experimental results, and being able to write and speak about them and defend them in a public forum. It is desired that students be allowed to work as independently as possible. Particular emphasis is placed on the keeping of good laboratory records that contain all the components of a scientific publication, and also of a Diplom thesis: an introduction, experimental section, results, discussion, and summary.
Each student is required to give a 20 to 30 minute lecture about his or her experiment. This gives them the opportunity to practice skills needed for a successful oral defense. In addition 24 other experiments must be tried and will be listed in the "Testat" certificate.

Laboratory Practicum I: Overview ( Runaround Practicum)

W	6	8 cr

In this practicum, the experiments are conducted on the research apparatuses of each professor's laboratory. As such, the procedures are based on problems that are within a field of interest of the Institute faculty. This allows students to acquaint themselves with the Institute's offerings and to begin deciding on their own area of specialization for their Diplom thesis. Students are allowed to choose freely among the experimental setups; however, it is required that each experiment be done in a different faculty member's laboratory and that at least one experiment be in theoretical physics.
In order to emphasize the link between theoretical and experimental physics, the instructors of the theoretical physics courses will provide students with exercises that are relevant to the experimental areas of research of the department.
As in the Advanced Practicum, students are expected to keep accurate laboratory notebooks and will also be given 20 to 30 minutes for an oral presentation to explain and defend their work on one experiment of their choice. A total of seven experiments must be performed; each will be certified with a "Testat".

Laboratory Practicum II: Specialization

S	6	12 cr

During this semester, students work in a research group of their choice on a project that is usually on the cutting edge of physics. The project may be on the same subject as the Diplom thesis that begins in the subsequent semester. However, the choice of this Practicum's topic and that of the Diplom topic are completely independent of one another. The time in which the Practicum project should be completed is agreed upon by the student and the project advisor.
The results of this Practicum project must be reported in written form, in a word-processed document, and also in a 20- to 30-minute oral presentation.