Syllabus
Groups and subgroups, group order, left and right classes, classes of conjugated elements, group homomorphisms and isomorphism. Direct product of groups.
Group representations. Reducible and irreducible representations.
Characters. Orthogonality relations.
Symmetry in Quantum theory. Hamiltonian invariance under coordinate transformations.
Molecular symmetry group and symmetry elements. Point groups.
Tables of irreducible point-group representations. Vector space of molecular states and its decomposition into subspaces invariant under the action of molecular symmetry group.
Use of projection operators for construction of symmetry adapted bases. Hamiltonian matrix factorization.
Classification of quantum states with respect to irreducible representations. Symmetry and energy level degenarations.
Splitting of energy levels caused by lower degree of symmetry. Selection rules.
Molecule vibrations. Infrared spectra.
This course is suitable for diploma students and doctoral students.
Annotation
Analysis of molecular symmetry by means of group theory. Groups of symmetry transformations and their representations.
Laws of conservation. Symmetry adapted functions.
Factorization of Hamiltonian. Quantum states classification in terms of symmetry.
Selection rules. Energy levels splitting caused by lower degree of symmetry.
Applications to studies of electronic structure and vibrations of molecules. The lecture is meant mainly for the students of physics of molecular and biological systems.