Advanced Quantum Theory (MVAMO2, MVSpec)

Contents

0. Introduction
   • A brief reminder of some basics of quantum mechanics
1. Quantum theory of matter
   • Identical particles
   • Bosons and fermions
   • Fock space
2. Interactions
   • Scattering theory
   • Potential scattering
   • Lippmann-Schwinger equation and Born approximation
   • Partial-wave expansion
   • Scattering cross section and optical theorem
   • Resonance scattering and bound states
   • Coulomb scattering
3. Theory of quantum states
   • Density matrix
   • Pure states and mixed ensembles
   • Environment and partial trace
   • Entanglement (EPR, Bell's inequalities)
   • Time evolution and thermalization
4. Open quantum systems
   • Markovian approximation and Lindblad Master equation
   • Jaynes-Cummings model
   • Collapse and revival
   • Adiabatic processes

Literature

There are many good textbooks on Quantum Mechanics, here are a few:

• Jean-Louis Basdevant, Jean Dalibard, Quantum Mechanics. Springer 2002.
• Claude Cohen-Tannoudji, Bernard Diu, Franck Laloë, Quantum Mechanics. Wiley, New York, 2005 (reprint). [ Google books | HEIDI ]
• L.D. Landau and E. M. Lifshitz, Quantum Mechanics. Non-relativistic theory. Pergamon Press, Oxford, 1977. [ HEIDI | Online Full Text ]
• F. Schwabl, Quantenmechanik I, II [in German]. Springer 2007. [ Ebook I | Ebook II ]
• N. Straumann, Quantenmechanik [in German]. Springer 2013. [ Ebook ]
• Steven Weinberg, Lectures on Quantum Mechanics. Cambridge University Press, 2nd ed., 2015. [ Google books | HEIDI ]

Fock space/Second quantization

• A. Altland, B. Simons, Condensed Matter Field Theory, 3rd ed., Cambridge 2023. In particular section 2.1. [ HEIDI ]

Scattering theory

• C.J. Joachain, Quantum Collision Theory. North-Holland, Amsterdam, 1983. [ HEIDI | Scribd Full Text ]
• Landau and Lifshitz (see above), see Chapters XVII & XVIII.
• J. Dalibard, Collisional dynamics of ultra-cold atomic gases. Varenna lecture notes 1998. [ Full Text ]

Open quantum systems

• M.D. Lukin, Modern Atomic and Molecular Physics II. Harvard lecture notes 2016. [ Full Text ]

Prerequisites

contents of PEP1-4, PTP1-4, in particular Quantum Mechanics (PTP4)