Applied Quantum Mechanics

German Research School for Simulation Sciences and RWTH Aachen University
WS 2016/17, Thu 09:15-11:45 and 13:15-15:45, Lecture Hall, GRS Jülich (CAMPUS page)
Do not forget to register for the exam through CAMPUS Office.
There will be no lecture/exercises on 12 January 2017 due to the International Workshop on Computational Physics and Materials Science


  1. Why Quantum Mechanics?
    Particle-waves and Schrödinger equation
    Particle in a box
    slides and exercises
    links to movies etc.:
  2. time-dependent Schrödinger equation
    probability interpretation and continuity equation
    separation of variables and time-independent Schrödinger equation
    initial value problem (Crank-Nicolson vs. eigenstate expansion)
    Gaussian wave packets (animation)
    slides and exercises
  3. piece-wise constant potentials
    matching of wave functions
    potential step, tunneling
    finite potential well (example: 20 Å wide, 4 eV deep; read off kn in Å)
    slides and exercises
  4. linear potentials and numerical solution of the Schrödinger equation
    linear potential and dimensionless units
    Airy functions (NIST Digital Library of Mathematical Functions)
    asymptotics of wave functions
    numerical solution: finite differences and Numerov trick
    stability of integration
    slides and exercises
  5. harmonic oscillator
    analytic solution, Hermite polynomials
    algebraic solution, ladder operators
    slides and exercises
  6. formalism of quantum mechanics
    measurement and expectation value
    Dirac notation, inner product, Hilbert space
    linear operators, inverse, unitary, Hermitian
    slides and exercises
  7. common eigenfunctions of commuting operators
    simultaneous diagonalization of operators
    uncertainty relations
    slides and exercises
  8. spherical symmetry and angular momentum
    spherical coordinates
    radial Schödinger equation
    angular momentum algebra
    slides and exercises
  9. spherical harmonics
    calculating spherical harmonics
    interactive visualization
    separation of two body-problem in center-of-mass and relative coordinates
    slides and exercises
  10. Xmas Lecture: Quantum Computing
    IBM Quantum Experience: Web access to IBM's 5-qbit quantum computer
    slides and tutorial (zip)
  11. hydrogen atom
    radial equation
    analytic solution, Laguerre polynomials
    atomic orbitals, periodic table
    self-consistent calculations for many-electron systems
    slides and exercises
    interactive page for calculating many-electron atoms
  12. perturbation theory
    first and second order, non-degenerate and degenerate
    slides and exercises
  13. time-dependent perturbation theory
    first order; harmonic perturbation, Fermi's golden rule
    slides and exercises
  14. basis sets and tight-binding
    chemical bonds: covalent, polar, ionic
    Born-Oppenheimer approximation
    Hellmann-Feynman theorem

Erik Koch