Dates:

Lecture: Tuesday 09:45 - 11:15 (Beginning 19.04.)

Tutorial: Monday 16:45 - 18:15 (Beginning 02.05, biweekly)

You find all information about the room and the problem sets in the Stud.IP-event, please register!

Dates:

Lecture: Monday 13:15 - 14:45 (Beginning 25.10.)

              Thursday 9:45 - 11:15

Tutorial: Monday 15:00 - 16:30

Link to the online lecture: In the Stud.IP-event, please register!

Submit the problem sets: At the start of the lecture on thursday

Dates:

Lecture: Monday 13:15 - 14:45 (Beginning 12.04.)

Tutorial: tba

Link to the online lecture: In the Stud.IP-event, please register!

Submit the problem sets to: jonas.sommerfeldt@ptb.de

Dates:

Lecture: Monday 13:15 - 14:45 (Beginning 19.10.)

Tutorial: tba

Link to the online lecture: In the Stud.IP-event, please register!

Submit the problem sets to: jonas.sommerfeldt@ptb.de

Dates:

Lecture/Tutorial:
Tuesday 9:45 - 10:30 (online)
Thursday 9:45 - 10:30 (online)

Please register in studip for the lecture

Dates:

Lecture: Monday 13:15 - 14:45 (Beginning 22.04.)

Tutorial: tba

Link to the online lecture: In the Stud.IP-event, please join it!

Submit the problem sets to: jonas.sommerfeldt@ptb.de

Lecture Notes:

Lecture 1 (22.04.2020) - Motivation and introduction
(Transparencies)

Lecture 2 (29.04.2020) - Basics of semi-classical theory of light-matter interaction
(Transparencies)

Lecture 3 (06.05.2020) - Rabi oscillations in semi-classical picture, Bloch sphere
(Transparencies)

Lecture 4 (20.05.2020) - Rabi oscillations in semi-classical picture, Bloch sphere
(Transparencies)

Lecture 5 (27.05.2020) - Quantization of the free electromagnetic field
(Transparencies)

Lecture 6 (03.06.2020) - Quantization of the free electromagnetic field
(Transparencies)

Lecture 7 (10.06.2020) - Fock states, creation and annihilation operators, quantum vacuum
(Transparencies)

Lecture 8 (17.06.2020) - Photon statistics, Coherent and squeezed states
(Transparencies)

Lecture 9 (24.06.2020) - Phase space formulation, coherent and squeezed states
(Transparencies)

Lecture 10 (29.06.2020) - Basics of “quantum” light-matter interaction, Basics of Jaynes-Cummings model
(Transparencies)

Lecture 11 (01.07.2020) - Time-dependent Jaynes Cummings model
(Transparencies)

Lecture 12 (08.07.2020) - Vacuum Rabi oscillations,dressed states
(Transparencies)

Lecture 13 (13.07.2020) - Quantum phenomena in lightatom interactions
(Transparencies)

Lecture 14 (15.07.2020) - Laser cooling, Magneto optical traps
(Transparencies)

Lecture 15 (22.07.2020) - Basic principle of quantum computers, q bits and quantum circuits
(Transparencies)

Problem sets:

Set 1 (Deadline 29.04.2020)

Set 2 (Deadline 13.05.2020)

Set 3 (Deadline 27.05.2020)

Set 4 (Deadline 17.06.2020)

Set 5 (Deadline 01.07.2020)

Set 6 (Deadline 15.07.2020)

Lecture Notes:

Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 5

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
(Transparencies)

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

Lecture 3 (28.10.2019) - Properties of angular momentum operators

Lecture 4 (28.10.2019) - Coupling of angular momenta

Lecture 5 (4.11.2019) - Clebsch-Gordan-coefficients: properties
(Transparencies)

Lecture 6 (11.11.2019) - Rotation in Euclidean space, rotation operator
(Transparencies)

Lecture 7 (14.11.2019) - Euler angles, Wigner D-matrices
(Transparencies)

Lecture 8 (18.11.2019) - Irreducible tensor operators, Wigner-Eckart theorem
(Transparencies)

Lecture 9 (21.11.2019) - Properties of irreducible tensors, evaluation of matrix elements
(Transparencies)

Lecture 10 (25.11.2019) - Basics of scattering theory, Lippmann-Schwinger equation
(Transparencies)

Lecture 11 (28.11.2019) - Green's function, cross Section
(Transparencies)

Lecture 12 (02.12.2019) - Scattering amplitude, differential cross section
(Transparencies)

Lecture 13 (05.12.2019) - First Born approximation
(Transparencies)

Lecture 14 (09.12.2019) - Scattering by spherically-symmetric potentials, optical theorem
(Transparencies)

Lecture 15 (12.12.2019) - Optical theorem, scattering phases
(Transparencies)

Lecture 17 (19.12.2019) - S-wave scattering, cold atoms
(Transparencies)

Lecture 18 (06.01.2020) - Relativistic quantum mechanics, Klein-Gordon equation
(Transparencies)

Lecture 19 (09.01.2020) - Dirac equation, gamma matrices
(Transparencies)

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

Lecture 21 (16.01.2020) - Particle aniti-particle interpretation, hydrogen-like ions
(Transparencies)

Lecture 22 (20.01.2020) - Spectrum of the hydrogen atom, relativistic corrections
(Transparencies)

Lecture 24 (27.01.2020) - Transformation between basis, field operators
(Transparencies)

Lecture 25 (30.01.2020) - Representation of operators in second quantization
(Transparencies)

Problem Sets:

Set 1 (Deadline 28.10.2019) - QM1 revisited

Set 2 (Deadline 04.11.2019) - Hermitian operators and angular momenta

Set 3 (Deadline 11.11.2019) - Angular momentum operators and coupling of angular momenta

Set 4 (Deadline 18.11.2019) - Quantum mechanical rotations

Set 5 (Deadline 25.11.2019) - Irreducible tensors

Set 6 (Deadline 02.12.2019) - Reduced matrix elements, Green's function

Set 7 (Deadline 09.12.2019) - 1st Born approximation and Lippmann-Schwinger equation

Set 8 (Deadline 16.12.2019) - Spherical Bessel functions

Set 9 (Deadline 06.01.2020) - Partial wave expansion

Set 10 (Deadline 13.01.2020) - Klein-Gordon equation

Set 11 (Deadline 20.01.2020) - Dirac equation

Set 12 (Deadline 27.01.2020) - Dirac equation

Link zu den Prüfungsterminen

Termine:

Vorlesung:
Montags 13:15 - 14:45 (3.318)

Übung:
Dienstags 9:45 - 11:15 (3.318) (14 tägig)

Skript:

Vorlesung 1 (08.04.2019) - Motivation
(Folien)

Vorlesung 2 (15.04.2019) - Grundlagen der semiklassischen Theorie der Licht-Materie-Wechselwirkung
(Folien)

Vorlesung 3 (16.04.2019) - Übergangswharscheinlichkeit atomarer Übergänge in der semiklassischen Theorie
(Folien)

Vorlesung 4 (29.04.2019) - Quantisierung des elektromagnetischen Feldes, Fock Zustände, Quantenvakuum
(Folien)

Vorlesung 5 (06.05.2019) - Kohärente Zustände und gequtschtes Licht

Vorlesung 6 (13.05.2019) - Grundlagen der Licht-Materie-Wechselwirkung und des  Jaynes-Cummings Models

Vorlesung 7 (20.05.2019) - Zeitabhängiges Jaynes-Cummings Model
(Folien)

Vorlesung 8 (27.05.2019) - Rabi-Oszillationen im semiklassischen Bild, Bloch-Kugel
(Folien)

Vorlesung 9 (03.06.2019) - Vakuum-Rabi-Oszillationen, dressed states
(Folien)

Vorlesung 10 (17.06.2019) - Quantenphänomene der Licht-Materie-Wechselwirkung
(Folien)

Vorlesung 11 (24.06.2019) - Laserkühlung und Magneto-optische Falle
(Folien)

Vorlesung 12 (01.07.2019) - Bose-Einstein-Kondensat

Vorlesung 13 (08.07.2019) - Quantencomputer, Qubits und Quantenschaltkreis
(Folien)

Vorlesung 14 (15.07.2019) - Quantencomputer und ihre Anwendungen

Übungsserien:

Serie 1 (Abgabe am 15.04.2019)

Serie 2 (Abgabe am 29.04.2019)

Serie 3 (Abgabe am 13.05.2019)

Serie 4 (Abgabe am 27.05.2019)

Serie 5 (Abgabe am 02.07.2019)

Dates:

Please follow the link to choose an examination date!
Examination 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
(Transparencies)

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

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

Lecture 4 (08.11.2018) - First relativistic corrections to hydrogen-like ions

Lecture 5 (15.11.2018) - Energies and wave-functions of hydrogen-like ions (1)
(Transparencies)

Lecture 6 (22.11.2018) - Isotope shifts

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

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

Lecture 9 (13.12.2018) - Independent particle model

Lecture 10 (20.12.2018) - Central field approximation
(Transparencies)

Lecture 11 (10.01.2019) - Thomas Fermi Atome

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

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

Lecture 14 (01.02.2019) - Path integrals

Problem sets:

Set 1 (Discussion at 25.10.2018)

Set 2 (Discussion at 05.11.2018)

Set 3 (Discussion at 19.11.2018)

Set 4 (Discussion at 03.12.2018)

Set 5 (Discussion at 17.12.2018)

Set 6 (Discussion at 14.01.2018)
Solution

Set 7 (Discussion at 28.01.2018)
Mathematica Notebook

Dates:

Please follow the link to choose an examination date!

Examination date

Lecture:

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

Tutorial (biweekly):

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

Lecture Notes:

Lecture 1 (09.04.2018) - Motivation, Maxwell equations
(Transparencies)

Lecture 2 (16.04.2018) - Maxwell-Schroedinger equation, Time dependent perturbation theory
(Transparencies)

Lecture 3 (23.04.2018) -  One-photon transition probabilities, electric dipole approximation
(Transparencies)

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

Lecture 5 (07.05.2018) - Electric dipole approximation, selection rules, spin of photon
(Transparencies)

Lecture 6 (28.05.2018) -  Bound-electron dynamics in EM fields, Rabi oscillations, Bloch sphere
(Transparencies)

Lecture 7-8 (04.06.2018) - Photoionization

Lecture 9 (11.06.2018) -  Scattering of light
(Transparencies)

Lecture 10 (18.06.2018) -  Scattering of light (2)
(Transparencies)

Lecture 11 (25.06.2018) - Twisted light

Lecture 12-13 (02.07.2018) - Free electrons in strong electromagnatic fields

Lecture 14 (09.07.2018) -   Modern light-matter interaction studies: Short overview
(Transparencies)

Problem sets:

Set 1 (Discussion at 23.04.2018): Isotope shift and weak fields
(Mathematica Notebook)

Set 2 (Discussion at 07.05.2018): Energy density, dipole approximation

Set 3 (Discussion at 18.06.2018): Photoionization, radiative recombination

Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 5

Lecture 6

Exam questions (last update 02.03.2018)

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:

Lecture 0 (16.10.2017) - Introduction

Lecture 1 (19.10.2017) - Angular momentum operator: Definition and properties
(Transparencies)

Lecture 2 (23.10.2017) - Angular momentum operator: Eigenvalues and eigenfunctions
(Transparencies)

Lecture 3 (26.10.2017) - Coupling of angular momenta, Clebsch-Gordan coefficients
(Transparencies)

Lecture 4 (30.10.2017) - Coupling of angular momenta, Clebsch-Gordan coefficients (II)
(Transparencies)

Lecture 5 (02.11.2017) - Explicit form and properties of Clebsch-Gordan coefficients
(Transparencies)

Lecture 6 (06.11.2017) - Rotations in euclidean space
(Transparencies)

Lecture 7 (09.11.2017) - Rotation operator, Euler angles
(Transparencies)

Lectures 8 & 9 (13.11.2017) - Wigner-D matrices and irreducible tensors
(Transparencies)

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

Lecture 11 (23.11.2017) - Basics of scattering theory, Lippmann-Schwinger Equation
(Transparencies)

Lecture 12 (27.11.2017) - Born approximation, Feynman diagrams
(Transparencies)

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

Lecture 14 (04.12.2017) - Time dependent scattering theory, wave packets
(Transparencies)

Lecture 15 (07.12.2017) - Møller-operator and S-operator
(Transparencies)

Lecture 16 (11.12.2017) - S-Matrix: Derivation and properties
(Transparencies)

Lecture 17 (14.12.2017) - Calculation of cross sections in time dependent scattering
(Transparencies)

Lecture 18 (18.12.2017) - Born perturbation theory
(Transparencies)

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)

Lecture 22 (15.01.2018) - Operators in second quantization
(Transparencies)

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

Lecture 24 (22.01.2018) - Relativistic quantum mechanics, Klein-Gordon equation
(Transparencies)

ÜbungsSetn:

Set 0 (no deadline) - Quantum mechanics 101

Set 1 (Abgabe: 26.10.2017) - Properties of hermitian and angular momentum operators

Set 2 (Abgabe: 02.11.2017) - Coupling of angular momenta, Pauli matrices

Set 3 (Abgabe: 09.11.2017) - Angular momentum coupling in two-particle systems

Set 4 (Abgabe: 16.11.2017) - Rotations in euclidean space, irreducible tensors

Set 5 (Abgabe: 23.11.2017) - Reduced matrix elements, Green's function

Set 6 (Abgabe: 30.11.2017) - Green's function, Lippmann-Schwinger equation

Set 7 (Abgabe: 07.12.2017) - Born approximation

Set 8 (Abgabe: 14.12.2017) - Scattering of wave packets
Hinweise zu Aufgabe 3

Set 9 (Abgabe: 21.12.2017) - Properties of wave packets

Set 10 (Abgabe: 18.01.2018) - Two-particle systems

Set 11 (Abgabe: 25.01.2018) - Second quantization

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:

Lecture 0 (17.10.2016) - Introduction

Lecture 1 (20.10.2016) - Angular momentum operator: Definition and properties
(Transparencies)

Lecture 2 (24.10.2016) - Angular momentum operator: Eigenvalues and eigenfunctions
(Transparencies)

Lecture 3 (27.10.2016) - Coupling of angular momenta, Clebsch-Gordan coefficitents
(Transparencies)

Lecture 4 (31.10.2016) - Explicit form of Clebsch-Gordan coefficients
(Transparencies)

Lecture 5 (03.11.2016) - Rotations in euclidean space, rotation operator
(Transparencies)

Lecture 6 (07.11.2016) - Euler angles, Wigner-D matrix
(Transparencies)

Lecture 7 (10.11.2016) - Irreducible tensors, Wigner-Eckardt theorem
(Transparencies)

Lecture 8 (14.11.2016) - Algebra of tensor operators, calculation of matrix elements
(Transparencies)

Lecture 9 (17.11.2016) - Basics of scattering theory, Lippmann-Schwinger equation
(Transparencies)

Lecture 10 (21.11.2016) - Scattering amplitude, Born series, Feynman diagrams
(Transparencies)

Lecture 11 (24.11.2016) - Born approximation, Yukawa potential, Rutherford scattering
(Derivation of the total cross section for the scattering on a Yukawa potential)
(Transparencies)

Lecture 12 (28.11.2016) - Partial waves
(Transparencies)

Lecture 13 (01.12.2016) - Multipole expansion, optical theorem
(Transparencies)

Lecture 14 (04.12.2016) - Low energy scattering, s-wave scattering, cold atoms
(Transparencies)

Lecture 15 (08.12.2016) - Time dependent scattering theory, wave packets
(Transparencies)

Lecture 16 (12.12.2016) - S-operator and S-matrix
(Transparencies)

Lecture 17 (15.12.2016) - Born scattering theory
(Transparencies)

Lecture 18 (09.01.2017) - Identical particles: Bosons and fermions, Helium
(Transparencies)

Lecture 19 (12.01.2017) - Second quantization, Creation and annihilation operators
(Transparencies)

Lecture 20 (16.01.2017) - Field operators
(Transparencies)

Lecture 21 (19.01.2017) - Bose-Einstein condensates in second quantization

Lecture 22 (23.01.2017) - Bose-Einstein condensates in second quantization (cntd.)

Lecture 23 (26.01.2017) - Relativistic spinless particles, Klein-Gordon equation
(Transparencies)

Lecture 24 (02.02.2017) - Solutions of the free Dirac equation

Lecture 25 (06.02.2017) - Relativistic description of hydrogen like ions

Lecture 26 (09.02.2017) - Relativistic description of hydrogen like ions (cntd.)
(Transparencies)

ÜbungsSetn:

Set 0 (Präsenzübung) - Grundlegendes zum Formalismus der Quantenmechanik

Set 1 (Deadline: 27.10.2016) - Eigenschaften von hermiteschen und Drehimpulsoperatoren

Set 2 (Deadline: 03.11.2016) - Kopplung von Drehimpulsen, Pauli Matrizen

Set 3 (Deadline: 10.11.2016) - Drehimpulskopplung in Zweiteilchensystemen

Set 4 (Deadline: 17.11.2016) - Drehungen im euklidischen Raum, irreduzible Tensoren
(Mathematica Notebook and Python Skript for Task 1)

Set 5 (Deadline: 24.11.2016) - Reduzierte Matrixelemente, die Green'sche Funktion

Set 6 (Deadline: 01.12.2016) - Die Born'sche Näherung und zwei Beispiele
(Mathematica Notebook and Python Skript for Task 1)

Set 7 (Deadline: 08.12.2016) - Partialwellenzerlegung

Set 8 (Deadline: 15.12.2016) - Green-Operator und Streulänge

Set 9 (Deadline: 12.01.2017) - Wellenpakete und Störungstheorie

Set 10 (Deadline: 19.01.2017) - Stationäre Näherungsverfahren

Set 11 (Deadline: 26.01.2017) - Feldoperatoren

Set 12 (Deadline: 02.02.2017) - Spezielle Relativitätstheorie, Klein-Gordon Gleichung