21 330 V/U
(3+1)
Lectures and exercises:
V:
U:
This course is intended for international Master students. It is based
on knowledge of the necessary mathematics i.e. elementary analysis
(differentiation and integration) and linear algebra (matrices and vectors).
The aim of this facultative course is to prepare the students to the obligatory
course of Quantum Chemistry.
The
lectures and exercises are offered in English.
Irrational
numbers; Limits; Derivative; Series; Trigonometric functions; Fourier series;
Complex numbers; Periodicity.
Classical Mechanics
Schroedinger Equation
Energy as a Constant of the Motion; Wave Function; Schrödinger's Equation of
Motion; Operators; Probability Function; Eigenvalues and Eigenfunctions; Mean
value; Uncertainty Principle.
Motion of a quantum particle
Free particle traveling in an unbounded one-dimensional region; Infinitely
Thick Potential Wall; Boundary Conditions; Flux Density; Finite Width Barrier;
Particle in a box.
Hydrogen Atom
SIMPLE MODELS: Particle on a ring; Polar coordinates; Angular momentum;
Particle on a sphere; Rigid rotor.
HYDROGENIC WAVEFUNCTION: Radial wavefunction; Spherical harmonics; Atomic
orbitals; Quantum numbers; Helium atom.
Perturbation Theory
MATH: Vectors; Matrixes; Eigenvectors and eigenvalues; Bra and ket vectors.
PERTURBATION THEORY: Perturbed wavefunctions; Many-level system; Orders of
correction.
VARIATION METHODS: Fixed trial
functions; variable trial functions.
Literature:
Introduction to quantum mechanics with applications to chemistry
Dover Publ., Inc., NY, 1985
Molecular quantum mechanics
Oxford university press Inc., NY, 2005
Evaluation:
To pass the course, it is necessary to accumulate 50 % of the points in two
examinations. The first one in the middle and the second one at the end of the
course.
Notes: