MathMods :: Joint MSc

Additional Info

• ECTS credits: 6
• University: Gdansk University of Technology
• Semester: 3
• Lecturer 1: Maciej Bobrowski
• Lecturer 2: Sergey Kshevetskyy
• Objectives:

   

  During this course the students will study basic principles of quantum chemistry and electronic structure of molecules and solids. A wide spectrum of methods, from semi-empirical to self-consistent ones, and methods of calculation of band structures and density of states will be presented. Particular stress will be posed on practical practical aspects i.e. the capacity to choose the most proper computational method for given problem.

• Topics:

   

  1. Axioms of quantum mechanics

  2. Exact solutions of Schrodinger equation:
  a. free particle (in one dimension)
  b. particle in box (one- and two-dimensional)
  c. harmonic oscillator (one-dimension)
  d. rigid rotor (two- and three-dimensional)
  e. hydrogen atom (separation of motion of the center of mass, solutions - orbitals (s, p(x,y,z), d(5
  orbitals), energies, quantum numbers, radial density of probability, average distance of
  electron from nuclei, average kinetic energy)
  f. variational method: optimization of parameter c in trial function f(r,c) = exp(-cr) (expected
  values of hamiltonian and variational calculation).

  3. Periodic quantum systems (Bloch states, SF, HF, band theory, APW, KKR, DFT, etc.)
  a. The molecule and crystal Hamiltonians
  b. The Born-Oppenheimer approximation
  c. The variational principle
  d. Spin. The Slater determinant
  e. The Hartree-Fock equations
  f. The Roothan equations
  g. The Hartree-Fock equations
  h. The density functional theory
  i. The Bloch theorem. Common principles of solving the problems of zones. Dispersion equation
  j. The Kronig-Penney model of a crystal. Conductors, insulators, semiconductors.
  k. Electrons in empty lattice. The Fermi energy.
  l. Computer practice in computer solving of equations of quantum mechanics
  m. The model of weakly bond electrons
  n. Computer practice in solving of equations of quantum mechanics
  o. The model of tightly bond electrons