Teaching

Program of the course:

Mo 20.10.2025:  Introduction to quantum mechanics. Historical and experimental foundations. (Chapter 1 in QM – Schwabl)

Tue 21.10.2025: The wavefunction and the Schrödinger Equation. (Chapter 2 (2.1, 2.2, 2.3) in QM – Schwabl)

Mo 27.10.2025:  The wavefunction and the Schrödinger Equation: (Chapter 2 (2.4) in QM – Schwabl)

Tue 28.10.2025:  Operators and Scalar Product (Chapter 2.4.3 Schwabl), Correspondence principle, (Chapter 2 (2.5 in QM – Schwabl)

Mo 03.11.2025: Ehrenfest theorem, the continuity equation, stationary Solutions of the Schrödinger Equation, Eigenvalue Equations (Chapter 2.6, 2.7, 2.8 in QM Schwabl)

Tue 04.11.2025: The Harmonic Oscillator: The Algebraic Method (Chapter 3.1 in QM, Schwabl)

Mo 10.11.2025: The Hermite Polynomials; the Zero Point Energy; Coherent States (Chapter 3.1.2, 3.1.3, 3.1.4. in QM, Schwabl)

Tue 11.11.2025: The potential Step (Chapter 3.2 in QM, Schwabl)

Mo 17.11.2025: The potential barrier and the tunnelling effect;  the potential Well (Chapter 3.3.1; 3.4 in QM, Schwabl)

Tue 18.11.2025: Parity operator (Chapter 3.5.1  in QM, Schwabl); The Potential Well, Resonances (Chapter 3.7 pages 81-83) The Heisenberg Uncertainty Relation (Chapter 4.1; in QM, Schwabl)

Mo 24.11.2025: Common Eigenfunctions of Commuting Operators (Chapter 4.3; in QM, Schwabl) 

Tue 25.11.2025: Angular Momentum: Commutation Relations, Rotations (Chapter 5.1 in QM, Schwabl); Eigenvalues of Angular Momentum Operators; Orbital Angular Momentum in Polar Coordinates. (Chapter 5.2 and 5.3  in QM, Schwabl)

Mo 01.12.2025: The central potential: Spherical Coordinates, Bound States in Three Dimensions  (Chapter 6.1; 6.2  in QM, Schwabl); The Coulomb Potential  (Chapter 6.3  in QM, Schwabl)

Tue 02.12.2025: The Experimental Discovery of the Internal Angular Momentum; Mathematical Formulation for Spin-1/2; Properties of the Pauli Matrices; Magnetic Moment;  Addition of Spin-1/2 Operators; Orbital Angular Momentum and Spin 1/2 (Chapter 9.1; 9.2; 9.3;9.5 and 10.2; 10.3 in QM, Schwabl)

Mo 08.12.2025: Time independent perturbation theory (non-degenerate case); Variational principle (Chapter 11.1 and 11.2 in QM, Schwabl).

Tue 09.12.2025: Several electrons atoms: Identical particles; Helium; the Hartree-Fock approximation (13.1, 13.2 and 13.3  in QM, Schwabl)

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Description:

Classical molecular dynamics (MD): integrating algorithms, accuracy, thermostats and barostats, Ewald summation.

Monte Carlo and kinetic Monte Carlo: importance sampling, canonical ensemble, master equation.

Grand canonical simulations and free energy methods.

Quantum mechanical approaches and density functional theory.

Hands-on examples: MD simulations of the Lennard-Jones fluid, MD simulations of biomolecules, Ising model.

Lecture dates: Monday 10:15-11.45 room NB 7/173 and Friday 10:15-11:45 room NB 7/173

Exercise dates: Thursdays 9:15-10:45 room NB 6/73

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