German Research School for Simulation Sciences and RWTH Aachen University (RWTHonline)
Lectures Thu 09:30-12:00 and Exercises 13:15-15:45, Lecture Hall, GRS Jülich
Lectures
Why Quantum Mechanics?
Particle-waves and Schrödinger equation:    time-dependent (initial value problem), time-independent (eigenvalue problem)
Particle in a box (example: ground state energy for L=1nm: google (hbar*pi/1 nm)^2/(2*electron mass) in eV)
reading: Griffiths Sec. 1.1, 1.2, 2.1, 2.2 slides and exercises links to movies etc.:
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, Numerical Recipes Sec. 19.2)
Gaussian wave packets (animation)
reading: Schwabl Sec. 2.7, 2.3, 2.10.2 or Griffiths Sec. 2.4
slides and exercises
piece-wise constant potentials
matching of wave functions
potential step, tunneling
finite potential well (example: 20 Å wide, 4 eV deep:
google x*tan(x*20/2), -x/tan(x*20/2), sqrt((0.262468435*4)-x^2)
and read off kn in Å-1
reading: Schwabl: Sec. 3.2, (3.3), 3.4, Griffiths 2.5 slides and exercises
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
reading: Griffiths Sec 8.3 and Schwabl Sec. 3.6 slides and exercises
harmonic oscillator
analytic solution, Hermite polynomials
algebraic solution, ladder operators
reading: Griffiths Sec. 2.3 or Schwabl Sec. 3.1 slides and exercises
formalism of quantum mechanics
measurement and expectation value
Dirac notation, inner product, Hilbert space
linear operators, inverse, unitary, Hermitian
reading: Griffiths Sec. 3.1-4+6, Schwabl Sec. 8.1-3 slides and exercises
common eigenfunctions of commuting operators
simultaneous diagonalization of operators
uncertainty relations
reading: Schwabl Sec.4.1/3, Griffiths Sec. 3.5 slides and exercises
spherical symmetry and angular momentum
spherical coordinates
radial Schödinger equation
angular momentum algebra
reading: Griffiths Sec. 4.1 or Schwabl Sec. 5.3, 6.1 slides and exercises
hydrogen atom
radial equation
analytic solution, Laguerre polynomials
atomic orbitals, periodic table
self-consistent calculations for many-electron systems
reading: Griffiths Sec. 4.2 or Schwabl Sec. 6.3/4 slides and exercises interactive page for calculating many-electron atoms
perturbation theory
first and second order, non-degenerate and degenerate
reading: Griffiths Sec. 6.1/2 or Schwabl Sec. 11.1 slides and exercises
time-dependent perturbation theory
first order; harmonic perturbation, Fermi's golden rule
reading: Griffiths Ch. 9 or Schwabl Sec. 16.3 slides and exercises
basis sets and tight-binding
chemical bonds: covalent, polar, ionic
Born-Oppenheimer approximation
Hellmann-Feynman theorem slides
Simulation Science: Physics Focus lectures
and more