Advanced quantum mechanics
FSU Jena, WS 2022
Lecture period: 17.10.2021 - 10.02.2023
Last updated: 12.09.2022
Moodle link
Moodle link tutorials
Topics
- Postulates
- Introduction: Stern-Gerlach experiments
- State vectors and operators
- Observables and measurements
- Uncertainty relations
- Time evolution
- Schroedinger equation and formal solutions (Dyson series)
- Energy eigenvectors, evolution of expectation values and correlation amplitudes
- Heisenberg picture
- Transition amplitudes
- Propagator
- Path integral
- Interaction with classical EM field
- Minimal coupling Hamiltonian
- Gauge transformation
- Particle in a constant magnetic field
- Landau levels and Hall effect
- Aharonov-Bohm effect
- Theory of angular momentum
- Angular momentum as generator of rotation
- Eigenvalues and eigenstates
- Matrix elements
- Pauli formalism for spin 1/2
- Addition of angular momenta
- Tensor operators
- Wigner-Eckart theorem and selection rules
- Time-independent perturbation theory
- Stationary perturbation: nondegenerate case
- Asymptotic series
- Feynmann-Helman theorem
- Stationary perturbation: degenerate case
- H-atom in uniform electric field: Stark effects
- Parity operator
- Fine structure of the H atom
- Hyperfine structure of the H atom
- Time-dependent perturbation theory
- Interaction picture
- Two-state problems
- Time-depedent perturbation formalism
- Harmonic perturbations
- Transition rates and Fermi's golden rule
- Absorption and stimulated emission
- Spontaneous emission and black body spectrum
- Photoelectric effect
- Scattering formalism
- Lippmann-Schwinger equation
- Scattering amplitude
- Transition rate and S-matrix
- Differential cross section
- Born series
- Partial waves
- Low-energy scattering
- WKB approximation (*)
- Resonances (*)
- Electron-atom scattering
- Ensambles and Quantum Statistical Mechanics
- Pure, random and mixed ensambles
- Ensamble average
- Density operator and its time evolution
- Ensamble in thermal equilibrium and canonical ensamble
- Many body systems
- Hilbert space for many particles
- Identical particles
- Symmetrization postulate
- Two electrons system
- Variational method
- He atom
- Hartree-Fock approximation
- Fock space and second quantization
- Relativistic quantum mechanics
- Klein-Gordon equation
- Particles and antiparticles
- Dirac equation
- Conserved current
- Free particle solution
- H-atom (*)
- Coupling to electromagnetic field and electron magnetic moment (*)
(*) Optional/Supplementary material. It will be discussed only if time will permit.
Literature
- J.J. Sakurai "Modern Quantum Mechanics; 2.Ed" Pearson (1993)
- G.Baym "Lectures on Quantum Mechanics" Addison-Wesley Publishing (1990)
- D.J.Griffiths "Introduction to quantum mechanics" Cambridge University Press (2005)
- C.Cohen-Tannoudij, B. Diu and F. Laloe; “Quantum Mechanics I+II”, John Wiley & Sons
- S.Weinberg "Lectures on Quantum Mechanics" Cambridge University Press (2015)
- P.A.M Dirac "The Principles of Quantum Mechanics" Oxford University Press (1930)
- M.Bartelmann, B. Feuerbacher, T. Krüger, D. Lüst, A. Rebhan, A. Wipf, "Theoretische Physik", Springer (2014)
- Wipf's lecture notes
- G.Gottfried and T.M. Yan, “Quantum Mechanics: Fundamentals”, Springer
- Feynman Lectures On Physics - Vol. 3: "Quantum Mechanics" Feynman's lectures on physics website
- Fitzpatrick's online notes
Evaluation
- Exercise sheets will be distributed every week and corrected during the tutorials.
- We plan three intermediate tests (end of Nov, Dec-Jan, Jan).
- Admission to exam requires to collect more than 60% of the points from the intermediate tests.
- The exam will be in written form.
YouTube & web resources