KIP > SynQS > Gasenzer GroupTeachingSS 16: Advanced Quantum Theory

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.):
  1. Introduction
    - A brief reminder of some basics of quantum mechanics
  2. 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
  3. 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
  4. 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
  5. 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.