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We are seeking highly motivated and enthusiastic students aiming to make their Bachelor and/or Master thesis is theoretical physics. We offer a number of Bachelor and Master Projects related to the development of novel metrology standards, determination of the fundamental physical constants, and studies of the basic symmetries of Nature.  The studies will be performed in a close collaboration with theoretical and experimental groups both at the PTB and the Technical University of Braunschweig as well as world-wide.

Current projects:

  • Application of vortex photon beams in metrology and nanotechnology
  • Nuclear excitation via atomic bridge processes
  • Dynamics of many-electron systems
  • Gravitational influences on optical and quantum systems

LecturesLectures

Quantum Theory II (WS 19/20)

Dates:

Lecture:
Monday 13:15 - 14:45 (MS 3.318)
Thursday 09:45 - 11:15 (MS 3.318)

Tutorial:
Monday 15:00 - 16:30 (MS 3.318)

Lecture Notes:

Lecture 1 (21.10.2019) - Introduction
(Initiates file downloadTransparencies)

Lecture 2 (24.10.2019) - Spatial symmetries in physics and chemistry, angular momentum operator
(Initiates file downloadTransparencies)

Initiates file downloadLecture 3 (28.10.2019) - Properties of angular momentum operators

Initiates file downloadLecture 4 (28.10.2019) - Coupling of angular momenta

Lecture 5 (4.11.2019) - Clebsch-Gordan-coefficients: properties
(Initiates file downloadTransparencies)

Lecture 6 (11.11.2019) - Rotation in Euclidean space, rotation operator
(Initiates file downloadTransparencies)

Lecture 7 (14.11.2019) - Euler angles, Wigner D-matrices
(Initiates file downloadTransparencies)

Lecture 8 (18.11.2019) - Irreducible tensor operators, Wigner-Eckart theorem
(Initiates file downloadTransparencies)

Lecture 9 (21.11.2019) - Properties of irreducible tensors, evaluation of matrix elements
(Initiates file downloadTransparencies)

Lecture 10 (25.11.2019) - Basics of scattering theory, Lippmann-Schwinger equation
(Initiates file downloadTransparencies)

Lecture 11 (28.11.2019) - Green's function, cross Section
(Initiates file downloadTransparencies)

Lecture 12 (02.12.2019) - Scattering amplitude, differential cross section
(Initiates file downloadTransparencies)

Lecture 13 (05.12.2019) - First Born approximation
(Initiates file downloadTransparencies)

Lecture 14 (09.12.2019) - Scattering by spherically-symmetric potentials, optical theorem
(Initiates file downloadTransparencies)

Lecture 15 (12.12.2019) - Optical theorem, scattering phases
(Initiates file downloadTransparencies)

Lecture 17 (19.12.2019) - S-wave scattering, cold atoms
(Initiates file downloadTransparencies)

Lecture 18 (06.01.2020) - Relativistic quantum mechanics, Klein-Gordon equation
(Initiates file downloadTransparencies)

Lecture 19 (09.01.2020) - Dirac equation, gamma matrices
(Initiates file downloadTransparencies)

Lecture 20 (13.01.2020) - Solutions of the free Dirac equation, particle aniti-particle interpretation
(Initiates file downloadTransparencies)

Lecture 21 (16.01.2020) - Particle aniti-particle interpretation, hydrogen-like ions
(Initiates file downloadTransparencies)

Lecture 22 (20.01.2020) - Spectrum of the hydrogen atom, relativistic corrections
(Initiates file downloadTransparencies)

Lecture 24 (27.01.2020) - Transformation between basis, field operators
(Initiates file downloadTransparencies)

Lecture 25 (30.01.2020) - Representation of operators in second quantization
(Initiates file downloadTransparencies)

Problem Sets:

Initiates file downloadSet 1 (Deadline 28.10.2019) - QM1 revisited

Initiates file downloadSet 2 (Deadline 04.11.2019) - Hermitian operators and angular momenta

Initiates file downloadSet 3 (Deadline 11.11.2019) - Angular momentum operators and coupling of angular momenta

Initiates file downloadSet 4 (Deadline 18.11.2019) - Quantum mechanical rotations

Initiates file downloadSet 5 (Deadline 25.11.2019) - Irreducible tensors

Initiates file downloadSet 6 (Deadline 02.12.2019) - Reduced matrix elements, Green's function

Initiates file downloadSet 7 (Deadline 09.12.2019) - 1st Born approximation and Lippmann-Schwinger equation

Initiates file downloadSet 8 (Deadline 16.12.2019) - Spherical Bessel functions

Initiates file downloadSet 9 (Deadline 06.01.2020) - Partial wave expansion

Initiates file downloadSet 10 (Deadline 13.01.2020) - Klein-Gordon equation

Initiates file downloadSet 11 (Deadline 20.01.2020) - Dirac equation

Initiates file downloadSet 12 (Deadline 27.01.2020) - Dirac equation

Previous LecturesPrevious Lectures



Quantum optics (SS19)

Link to exam's date

Dates:

Lecture:
Monday 13:15 - 14:45 (3.318)

Tutorial:
Tuesday 9:45 - 11:15 (3.318) (biweekly)

Lecture Notes:

Lecture 1 (08.04.2019) - Motivation
Initiates file download(Transparencies)

Lecture 2 (15.04.2019) - Basics of semi-classical theory of light-matter interaction
Initiates file download(Transparencies)

Lecture 3 (16.04.2019) - Probability of atomic transitions in semi-classical theory
Initiates file download(Transparencies)

Lecture 4 (29.04.2019) - Quantization of the free electromagnetic field, Fock states, quantum vacuum
Initiates file download(Transparencies)

Lecture 5 (07.05.2019) - Coherent and squeezed states

Lecture 6 (13.05.2019) - Basics of light-matter interaction in quantum picture, Basics of Jaynes-Cummings model

Lecture 7 (20.05.2019) - Time-dependent Jaynes-Cummings model
Initiates file download(Transparencies)

Lecture 8 (27.05.2019) - Rabi oscillations in semi-classical picture, Bloch sphere
Initiates file download(Transparencies)

Lecture 9 (03.06.2019) - Vacuum Rabi oscillations, dressed states
Initiates file download(Transparencies)

Lecture 10 (17.06.2019) - Quantum phenomena in light atom interactions
Initiates file download(Transparencies)

Lecture 11 (24.06.2019) - Laser cooling, Magneto optical traps
Initiates file download(Transparencies)

Lecture 12 (01.07.2019) - Bose-Einstein Condensates

Lecture 13 (08.07.2019) - Basic principle of quantum computers, qbits and quantum circuits
Initiates file download(Transparencies)

Lecture 14 (15.07.2019) - Quantum computers and their applications

Problem sets:

Initiates file downloadSet 1

Initiates file downloadSet 2

Initiates file downloadSet 3

Initiates file downloadSet 4

Initiates file downloadSet 5



Quantum matter II (WS 18/19)

Dates:

Please follow the link to choose an examination date!
Opens external link in new windowExamination date

Lecture:

Thursday 09:45 - 11:15 (MS 3.3)

Tutorial (biweekly):

Monday 09:45 - 11:15 (MS 3.3)

Lecture Notes:

Lecture 1 (15.10.2018) - Motivation
Initiates file download(Transparencies)

Lecture 2 (25.10.2018) - Interpretation of Dirac equation, equation for particle in field
Initiates file download(Transparencies)

Lecture 3 (29.10.2018) - Relativistic corrections of hydrogen atom, Pauli equation

Initiates file downloadLecture 4 (08.11.2018) - First relativistic corrections to hydrogen-like ions

Initiates file downloadLecture 5 (15.11.2018) - Energies and wave-functions of hydrogen-like ions (1)
Initiates file download(Transparencies)

Initiates file downloadLecture 6 (22.11.2018) - Isotope shifts

Lecture 7 (29.11.2018) - Hyperfine interaction and quantum electrodynamics (QED) effects
Initiates file download(Transparencies)

Lecture 8 (06.12.2018) -  Hyperfine interaction and quantum electrodynamics (QED) effects (2)
Initiates file download(Transparencies)

Lecture 9 (13.12.2018) - Independent particle model

Lecture 10 (20.12.2018) - Central field approximation
Initiates file download(Transparencies)

Initiates file downloadLecture 11 (10.01.2019) - Thomas Fermi Atome

Lecture 12 (17.01.2019) - Correlation effects: Configuration interaction and perturbative approaches
Initiates file download(Transperencies)

Lecture 13 (24.01.2019) - Correlation effects: Configuration interaction and perturbative approaches (2)

Lecture 14 (01.02.2019) - Path integrals

Problem sets:

Initiates file downloadSet 1 (Discussion at 25.10.2018)

Initiates file downloadSet 2 (Discussion at 05.11.2018)

Initiates file downloadSet 3 (Discussion at 19.11.2018)

Initiates file downloadSet 4 (Discussion at 03.12.2018)

Initiates file downloadSet 5 (Discussion at 17.12.2018)

Initiates file downloadSet 6 (Discussion at 14.01.2018)
Initiates file downloadSolution

Initiates file downloadSet 7 (Discussion at 28.01.2018)
Initiates file downloadMathematica Notebook

Light-Matter Interaction (SS 18)

Dates:

Please follow the link to choose an examination date!

Opens external link in new windowExamination date

Lecture:

Monday 13:15 - 14:45 (MS 3.318)

Tutorial (biweekly):

Monday 11:30 - 13:00 (MS 3.318)

 

Lecture Notes:

Initiates file downloadLecture 1 (09.04.2018) - Motivation, Maxwell equations
(Initiates file downloadTransparencies)

Initiates file downloadLecture 2 (16.04.2018) - Maxwell-Schroedinger equation, Time dependent perturbation theory
(Initiates file downloadTransparencies)

Initiates file downloadLecture 3 (23.04.2018) -  One-photon transition probabilities, electric dipole approximation
(Initiates file downloadTransparencies)

Lecture 4 (30.04.2018) -  One-photon transition probabilities, electric dipole approximation

Initiates file downloadLecture 5 (07.05.2018) - Electric dipole approximation, selection rules, spin of photon
(Initiates file downloadTransparencies)

Initiates file downloadLecture 6 (28.05.2018) -  Bound-electron dynamics in EM fields, Rabi oscillations, Bloch sphere
(Initiates file downloadTransparencies)

Lecture 7-8 (04.06.2018) - Photoionization

Initiates file downloadLecture 9 (11.06.2018) -  Scattering of light
(Initiates file downloadTransparencies)

Initiates file downloadLecture 10 (18.06.2018) -  Scattering of light (2)
(Initiates file downloadTransparencies)

Lecture 11 (25.06.2018) - Twisted light

Initiates file downloadLecture 12-13 (02.07.2018) - Free electrons in strong electromagnatic fields

Lecture 14 (09.07.2018) -   Modern light-matter interaction studies: Short overview
(Initiates file downloadTransparencies)

 

Problem sets:

Initiates file downloadSet 1 (Discussion at 23.04.2018): Isotope shift and weak fields
(Initiates file downloadMathematica Notebook)

Initiates file downloadSet 2 (Discussion at 07.05.2018): Energy density, dipole approximation

Initiates file downloadSet 3 (Discussion at 18.06.2018): Photoionization, radiative recombination

Quantum Theory II (WS 17/18)

Dates:

 

Lecture:

Monday 13:15 - 14:45 (MS 3.318)
Thursday 09:45 - 11:15 (MS 3.318)

 

Tutorial:

Monday 15:00 - 16:30 (MS 3.318)

The solved problem sets have to be handed in on thursdays prior to the lecture

 

Lecture notes:

Initiates file downloadLecture 0 (16.10.2017) - Introduction

Initiates file downloadLecture 1 (19.10.2017) - Angular momentum operator: Definition and properties
(Initiates file downloadTransparencies)

Initiates file downloadLecture 2 (23.10.2017) - Angular momentum operator: Eigenvalues and eigenfunctions
(Initiates file downloadTransparencies)

Initiates file downloadLecture 3 (26.10.2017) - Coupling of angular momenta, Clebsch-Gordan coefficients
(Initiates file downloadTransparencies)

Initiates file downloadLecture 4 (30.10.2017) - Coupling of angular momenta, Clebsch-Gordan coefficients (II)
(Initiates file downloadTransparencies)

Initiates file downloadLecture 5 (02.11.2017) - Explicit form and properties of Clebsch-Gordan coefficients
(Initiates file downloadTransparencies)

Initiates file downloadLecture 6 (06.11.2017) - Rotations in euclidean space
(Initiates file downloadTransparencies)

Initiates file downloadLecture 7 (09.11.2017) - Rotation operator, Euler angles
(Initiates file downloadTransparencies)

Initiates file downloadLectures 8 & 9 (13.11.2017) - Wigner-D matrices and irreducible tensors
(Initiates file downloadTransparencies)

Lecture 10 (20.11.2017) - Algebra of tensor operators, calculation of matrix elements

Initiates file downloadLecture 11 (23.11.2017) - Basics of scattering theory, Lippmann-Schwinger Equation
(Initiates file downloadTransparencies)

Initiates file downloadLecture 12 (27.11.2017) - Born approximation, Feynman diagrams
(Initiates file downloadTransparencies)

Lecture 13 (30.11.2017) - Born approximation, Feynman diagrams (2)
(Transparencies)

Initiates file downloadLecture 14 (04.12.2017) - Time dependent scattering theory, wave packets
(Initiates file downloadTransparencies)

Initiates file downloadLecture 15 (07.12.2017) - Møller-operator and S-operator
(Initiates file downloadTransparencies)

Initiates file downloadLecture 16 (11.12.2017) - S-Matrix: Derivation and properties
(Initiates file downloadTransparencies)

Initiates file downloadLecture 17 (14.12.2017) - Calculation of cross sections in time dependent scattering
(Initiates file downloadTransparencies)

Initiates file downloadLecture 18 (18.12.2017) - Born perturbation theory
(Initiates file downloadTransparencies)

Lecture 19 (08.01.2018) - Identical particles, complete (anti-)symmetric states
(Transparencies)

Lecture 20 (08.01.2018) - Second quantization: Creation and annihiliation operators
(Transparencies)

Lecture 21 (11.01.2018) - Transformation between basises
(Transparencies)

Initiates file downloadLecture 22 (15.01.2018) - Operators in second quantization
(Initiates file downloadTransparencies)

Lecture 23 (18.01.2018) - BEC, Bogolijubov-Approximation
(Transparencies)

Initiates file downloadLecture 24 (22.01.2018) - Relativistic quantum mechanics, Klein-Gordon equation
(Initiates file downloadTransparencies)

 

ÜbungsSetn:

Initiates file downloadSet 0 (no deadline) - Quantum mechanics 101

Initiates file downloadSet 1 (Abgabe: 26.10.2017) - Properties of hermitian and angular momentum operators

Initiates file downloadSet 2 (Abgabe: 02.11.2017) - Coupling of angular momenta, Pauli matrices

Initiates file downloadSet 3 (Abgabe: 09.11.2017) - Angular momentum coupling in two-particle systems

Initiates file downloadSet 4 (Abgabe: 16.11.2017) - Rotations in euclidean space, irreducible tensors

Initiates file downloadSet 5 (Abgabe: 23.11.2017) - Reduced matrix elements, Green's function

Initiates file downloadSet 6 (Abgabe: 30.11.2017) - Green's function, Lippmann-Schwinger equation

Initiates file downloadSet 7 (Abgabe: 07.12.2017) - Born approximation

Initiates file downloadSet 8 (Abgabe: 14.12.2017) - Scattering of wave packets
Initiates file downloadHinweise zu Aufgabe 3

Initiates file downloadSet 9 (Abgabe: 21.12.2017) - Properties of wave packets

Initiates file downloadSet 10 (Abgabe: 18.01.2018) - Two-particle systems

Initiates file downloadSet 11 (Abgabe: 25.01.2018) - Second quantization

Quantum Theory II (WS 16/17)

Dates:

 

Lecture:

Monday 13:15 - 14:45 (MS 3.318)
Thursday 09:45 - 11:15 (MS 3.318)

 

Tutorial:

Monday 15:00 - 16:30 (MS 3.318)

The solved problem sets have to be handed in on thursdays prior to the lecture

 

Lecture notes:

Initiates file downloadLecture 0 (17.10.2016) - Introduction

Initiates file downloadLecture 1 (20.10.2016) - Angular momentum operator: Definition and properties
(Initiates file downloadTransparencies)

Initiates file downloadLecture 2 (24.10.2016) - Angular momentum operator: Eigenvalues and eigenfunctions
(Initiates file downloadTransparencies)

Initiates file downloadLecture 3 (27.10.2016) - Coupling of angular momenta, Clebsch-Gordan coefficitents
(Initiates file downloadTransparencies)

Initiates file downloadLecture 4 (31.10.2016) - Explicit form of Clebsch-Gordan coefficients
(Initiates file downloadTransparencies)

Initiates file downloadLecture 5 (03.11.2016) - Rotations in euclidean space, rotation operator
(Initiates file downloadTransparencies)

Initiates file downloadLecture 6 (07.11.2016) - Euler angles, Wigner-D matrix
(Initiates file downloadTransparencies)

Initiates file downloadLecture 7 (10.11.2016) - Irreducible tensors, Wigner-Eckardt theorem
(Initiates file downloadTransparencies)

Initiates file downloadLecture 8 (14.11.2016) - Algebra of tensor operators, calculation of matrix elements
(Initiates file downloadTransparencies)

Initiates file downloadLecture 9 (17.11.2016) - Basics of scattering theory, Lippmann-Schwinger equation
(Initiates file downloadTransparencies)

Initiates file downloadLecture 10 (21.11.2016) - Scattering amplitude, Born series, Feynman diagrams
(Initiates file downloadTransparencies)

Initiates file downloadLecture 11 (24.11.2016) - Born approximation, Yukawa potential, Rutherford scattering
(Initiates file downloadDerivation of the total cross section for the scattering on a Yukawa potential)
(Initiates file downloadTransparencies)

Initiates file downloadLecture 12 (28.11.2016) - Partial waves
(Initiates file downloadTransparencies)

Initiates file downloadLecture 13 (01.12.2016) - Multipole expansion, optical theorem
(Initiates file downloadTransparencies)

Initiates file downloadLecture 14 (04.12.2016) - Low energy scattering, s-wave scattering, cold atoms
(Initiates file downloadTransparencies)

Initiates file downloadLecture 15 (08.12.2016) - Time dependent scattering theory, wave packets
(Initiates file downloadTransparencies)

Initiates file downloadLecture 16 (12.12.2016) - S-operator and S-matrix
(Initiates file downloadTransparencies)

Initiates file downloadLecture 17 (15.12.2016) - Born scattering theory
(Initiates file downloadTransparencies)

Initiates file downloadLecture 18 (09.01.2017) - Identical particles: Bosons and fermions, Helium
(Initiates file downloadTransparencies)

Initiates file downloadLecture 19 (12.01.2017) - Second quantization, Creation and annihilation operators
(Initiates file downloadTransparencies)

Initiates file downloadLecture 20 (16.01.2017) - Field operators
(Initiates file downloadTransparencies)

Initiates file downloadLecture 21 (19.01.2017) - Bose-Einstein condensates in second quantization

Initiates file downloadLecture 22 (23.01.2017) - Bose-Einstein condensates in second quantization (cntd.)

Initiates file downloadLecture 23 (26.01.2017) - Relativistic spinless particles, Klein-Gordon equation
(Initiates file downloadTransparencies)

Initiates file downloadLecture 24 (02.02.2017) - Solutions of the free Dirac equation

Initiates file downloadLecture 25 (06.02.2017) - Relativistic description of hydrogen like ions

Lecture 26 (09.02.2017) - Relativistic description of hydrogen like ions (cntd.)
(Initiates file downloadTransparencies)

 

ÜbungsSetn:

Initiates file downloadSet 0 (Präsenzübung) - Grundlegendes zum Formalismus der Quantenmechanik

Initiates file downloadSet 1 (Deadline: 27.10.2016) - Eigenschaften von hermiteschen und Drehimpulsoperatoren

Initiates file downloadSet 2 (Deadline: 03.11.2016) - Kopplung von Drehimpulsen, Pauli Matrizen

Initiates file downloadSet 3 (Deadline: 10.11.2016) - Drehimpulskopplung in Zweiteilchensystemen

Initiates file downloadSet 4 (Deadline: 17.11.2016) - Drehungen im euklidischen Raum, irreduzible Tensoren
(Initiates file downloadMathematica Notebook and Initiates file downloadPython Skript for Task 1)

Initiates file downloadSet 5 (Deadline: 24.11.2016) - Reduzierte Matrixelemente, die Green'sche Funktion

Initiates file downloadSet 6 (Deadline: 01.12.2016) - Die Born'sche Näherung und zwei Beispiele
(Initiates file downloadMathematica Notebook and Initiates file downloadPython Skript for Task 1)

Initiates file downloadSet 7 (Deadline: 08.12.2016) - Partialwellenzerlegung

Initiates file downloadSet 8 (Deadline: 15.12.2016) - Green-Operator und Streulänge

Initiates file downloadSet 9 (Deadline: 12.01.2017) - Wellenpakete und Störungstheorie

Initiates file downloadSet 10 (Deadline: 19.01.2017) - Stationäre Näherungsverfahren

Initiates file downloadSet 11 (Deadline: 26.01.2017) - Feldoperatoren

Initiates file downloadSet 12 (Deadline: 02.02.2017) - Spezielle Relativitätstheorie, Klein-Gordon Gleichung