Advanced Quantum Theory
Lecture (MVAMO2)
Thomas Gasenzer
Thursday, 11:15-13:00 (starting on 21/04);
INF 227 (KIP), SR 3.403+4.
[
LSF]
Additional lectures: Tuesday,
10/05 and
24/05; 14:15-16:00;
INF 227 (KIP), SR 1.403+4.
Exercises
Head tutor:
Asier Pineiro Orioli
Register and view group list here.
Classes take place in general during even weeks on
Tue, 14:15 - 16:00: INF 227 (KIP), SR 1.404;
Tue, 16:15 - 18:00: INF 227 (KIP), SR 2.402;
starting on 03/05/16.
Written exam on Wed, 27/07/15, 11:00-13:00 hrs, INF 227 (KIP), SR 3.403+4.
Content -
Prerequisites -
Script -
Literature -
Supplementary materials -
Exercises -
Exam
The lecture course provides an introduction to advanced quantum theory within the specialisation module Atomic, Molecular, and Optical Physics.
From the
MSc-Module handbook:
After completing this course the students will be able to
- describe the fundamental concepts of quantum physics and the relevant theoretical methods,
- analyse standard experimental approaches using the relevant theoretical methods,
- solve problems in quantum physics and quantum optics,
- apply the relevant theoretical methods to model concrete physical situations.
Content (prelim.):
-
Introduction
- A brief reminder of some basics of quantum mechanics
-
Quantum theory of matter
- From classical to quantum fields
- Lagrangian and Hamiltonian field theory
- *Constrained quantisation
- Quantisation of the Bose field
- Mode expansion
- Harmonic oscillator
- One- and multiparticle operators
- Fock space
- Identical particles
- Bosons and fermions
- Coherent states
- Wigner function and phase space
-
Interactions
- Born-Oppenheimer Approximation
- H+
2 and H2 molecules
- Potential scattering
- Scattering of a wave packet
- Green's function and Lippmann-Schwinger equation
- Scattering cross section
- Partial-wave analysis
- S-matrix and scattering phase
- *Long-range potentials
- Low-energy scattering and s-wave approximation
- Optical theorem
- Square-well potential: s-wave scattering length, effective range
- *Resonance scattering
-
Theory of quantum states
- Density operator
- Pure states and mixed ensembles
- Environment and partial trace
- The measurement process
- Alternative approaches
- Entanglement
- Einstein-Podolsky-Rosen Paradoxon
- Bell’s inequalities
-
Open quantum systems
- Quantization of the electromagnetic field
- Interaction of atoms with electromagnetic vacuum
- The Jaynes-Cummings model
- Collapse and revival
- Open quantum systems
- Dissipation in classical systems
- Master equation
- Spontaneous Emission
- Decoherence
Prerequisites:
-
Experimental Physics core courses (PEP 1-4), Theoretical Physics core courses (PTP 1-4)
(cf. MSc Module Manual)
Skriptum :
-
The notes will be available for download here, separately for each chapter.
Literature:
Textbooks on Quantum Mechanics (in alphabet. Order):
-
Gordon Baym,
Lectures on Quantum Mechanics.
Westview, Boulder, CO, u.a., 2010.
[ Google books
| HEIDI
]
-
Matthias Bartelmann, Björn Feuerbacher, Timm Krüger, Dieter Lüst, Anton Rebhan, und Andreas Wipf
Theoretische Physik.
Springer, Berlin, Heidelberg, 2015.
[ Google books
| HEIDI
| UB E-Book
]
-
Jean-Louis Basdevant, Jean Dalibard,
The Quantum Mechanics Solver: How to Apply Quantum Theory to Modern Physics.
Springer, Berlin, Heidelberg, 2013.
[ Google books
| HEIDI
| UB E-Book
]
-
Claude Cohen-Tannoudji, Bernard Diu, Franck Laloë,
Quantum Mechanics.
Wiley, New York, 2005 (Nachdr.).
[ Google books
| HEIDI
]
-
Thorsten Fliessbach,
Quantenmechanik:
Lehrbuch zur Theoretischen Physik III.
Springer, Berlin u.a., 2008.
[ Google books
| HEIDI
]
-
Gerald Grawert,
Quantenmechanik:
Studienbuch für Studierende der Physik, Mathematik und physikalischen Chemie.
Aula-Verlag, Wiesbaden, 1989.
[ HEIDI
]
-
Chris J. Isham,
Lectures on Quantum Theory.
Imperial College Press, World Scientific, Singapore, 2011.
[ Google books
| HEIDI
]
-
Lev D. Landau, Evgenij M. Lifschitz,
Quantenmechanik.
Harri Deutsch, Frankfurt am Main, 2007.
[ Google books
| HEIDI
]
-
Albert Messiah,
Quantenmechanik.
de Gruyter, Berlin u.a., 1991.
[ Google books
| HEIDI
]
-
Eugen Merzbacher,
Quantum Mechanics.
Wiley, New York, Chichester, Weinheim, 1998.
[ Google books
| HEIDI
]
-
Wolfgang Nolting,
Grundkurs Theoretische Physik 5/1+2. Quantenmechanik.
Springer, Berlin u.a., 2009, 2012.
[ Google books
| HEIDI Bd. 1/
2
| UB E-Book Bd. 1/
2
]
-
Jun John Sakurai, Jim Napolitano,
Modern Quantum Mechanics.
Addison-Wesley, Boston u.a., 2011.
[ Google books
| HEIDI
]
-
Franz Schwabl,
Quantenmechanik (QM I).
Springer, Berlin Heidelberg, 7. Aufl., 2007.
[ Google books
| HEIDI
| UB E-Book
]
-
Franz Schwabl,
Quantenmechanik für Fortgeschrittene (QM II).
Springer, Berlin Heidelberg, 5. Aufl., 2008.
[ Google books
| HEIDI
| UB E-Book
]
-
Steven Weinberg,
Lectures on Quantum Mechanics.
Cambridge University Press, 2nd ed., 2015.
[ Google books
| HEIDI
]
-
Steven Weinberg,
Quantenmechanik.
Pearson, Hallbergmoos, 1. Aufl., 2015.
[ Google books
| HEIDI
]
Classics:
-
Paul A. M. Dirac,
Principles of Quantum Mechanics.
Clarendon Press, Oxford University Press, Oxford, 2010.
[ Google books
| HEIDI
]
-
Werner Heisenberg,
Die physikalischen Prinzipien der Quantentheorie.
Bibl. Inst., Mannheim, 1968.
[ Google books
| HEIDI
]
-
John von Neumann,
Mathematische Grundlagen der Quantenmechanik.
Springer, Berlin, Heidelberg, 1996.
[ Google books
| HEIDI
]
-
Leonard I. Schiff,
Quantum Mechanics.
McGraw-Hill, Düsseldorf, u.a., 1968.
[ Google books
| HEIDI
]
Publicly accessible scripts:
-
Carlo Ewerz,
Vorlesung PTP4, Theoretische Quantenmechanik, Univ. Heidelberg, SS 2015 (in German)
[ webpage
]
-
Thomas Gasenzer,
Vorlesung PTP4, Theoretische Quantenmechanik, Univ. Heidelberg, SS 2013 (in German)
[ webpage
]
-
Richard Fitzpatrick,
Quantum Mechanics: A graduate level course, Lecture Notes, Univ. Texas Austin
[ pdf
]
-
Martin Plenio,
Quantum Mechanics, Lecture Notes, Imperial College, WT 2002
[ pdf
]
-
Timo Weigand,
Vorlesung PTP4, Theoretische Quantenmechanik, Univ. Heidelberg, SS 2011 (in German)
[ pdf
]
Classical Mechanics
-
Herbert Goldstein,
Klassische Mechanik.
Wiley-VCH, Weinheim, 2006.
[ Google books
| HEIDI
]
Quantization subject to (gauge) constraints
-
Marc Henneaux and Claudio Teitelboim,
Quantization of Gauge systems.
Princeton Univ. Press, Princeton, 1992.
[ Google books
| HEIDI
]
-
Roman Jackiw,
(Constraint) Quantization Without Tears.
Montepulciano, 1993.
[arXiv: hep-ph/9306075
]
Scattering theory
-
K. Burnett, P.S. Julienne, P.D. Lett, E. Tiesin, and C.J. Williams,
Quantum encounters of the cold kind.
Nature (London) 416, 225 (2002).
-
J. Dalibard,
Collisional dynamics of ultra-cold atomic gases.
Proc. Int. School Phys. Enrico Fermi, Course CXL: Bose-Einstein condensation in gases, Varenna 1998, M. Inguscio, S. Stringari, C. Wieman edts.
-
C.J. Joachain,
Quantum Collision Theory.
North-Holland, Amsterdam, 1983.
[ HEIDI
| Scribd Full Text
]
-
L.D. Landau and E. M. Lifshitz,
Quantum Mechanics. Non-relativistic theory. (see Chapters XVII & XVIII.)
Pergamon Press, Oxford, 1977.
[ HEIDI
| Online Full Text
]
-
R.G. Newton,
Scattering Theory of Waves and Particles.
Dover publications, 2002.
[ HEIDI
| Google Books
]
General texts on quantum optics
-
S.M. Barnett, P.M. Radmore,
Methods in Theoretical Quantum Optics,
Clarendon Press, Oxford, 1997.
[ HEIDI
]
-
C.W. Gardiner,
Quantum Noise.
2nd Ed.
Springer Verlag, Berlin, 2000.
[ HEIDI
]
-
L. Mandel, E. Wolf,
Optical Coherence and Quantum Optics, CUP, Cambridge, 2008 (ISBN 0-521-41711-2).
[ HEIDI
]
-
W.P. Schleich,
Quantum Optics in Phase Space.
Wiley-VCH, Weinheim, 2001.
[ HEIDI
]
-
M.O. Scully, M.S. Zubairy,
Quantum Optics.
CUP, Cambridge, 2008.
[ HEIDI
| Google Books
]
For further reference: A few general texts on quantum field theory
-
Brian Hatfield,
Quantum Field Theory of Point Particles and Strings.
Addison Wesley, Oxford, 2010.
[ Google books
| HEIDI
]
-
Michael E. Peskin, Daniel V. Schroeder
An introduction to quantum field theory.
Westview, Boulder, 2006.
[ Google books
| HEIDI
]
-
Xiao-Gang Wen,
Quantum Field Theory of Many-Body Systems.
OUP, Oxford, 2010.
[ Google books
| HEIDI
]
Additional material
Exercises:
Exercises will be during even weeks on
Tue, 14:15 - 16:00: INF 227 (KIP), SR 1.404;
Tue, 16:15 - 18:00: INF 227 (KIP), SR 2.402;
starting on 03/05/16. Tutors: Raphael Beinke and Salvatore Castrignano
(Please
register here.)
Problem Sheets will be available for
download here.
Exam:
Passing the written exam, which will prospectively take place on
Wed, 27/07/15, 11:00-13:00 hrs, INF 227 (KIP), SR 3.403+4,
will be the condition to obtain
4 CPs for the lecture.
Rules for the exam: You are allowed to use one A4 two-sided and handwritten sheet. No electronic devices of any kind are permitted. The exam lasts 120 mins. Please bring enough paper to be able to start every problem on a new sheet of paper.
