- Matrix formulation of quantum mechanics: Transformation, representations, projection
operators, equations of motion. Operator formalism: Virial theorem, model exactly solvable systems, Tunnelling effect: square barrier, WKB approximation, electron and proton transfer.
- Many-body problem: Many-body problem, Ant-symmetry and Slater Determinants, Variation and Perturbation methods, Born Oppenheimer approximation, Explicit derivation of Hartree and Hartree-Fock equations, Roothaan equations and introduction of basis sets STO and GTO, calculation of integrals, semi-empirical methods, Restricted versus unrestricted Hartree-Fock methods.
- Electron correlation problem: Electron correlation problem, Configuration interaction (CI) methods, singles and doubles CI, Size-consistency and size-extensivity, N dependence, Many-body methods , perturbation theory (MP-versions), diagrammatic representations and linked cluster theorem, coupled-cluster method. Brief overview of density functional theory
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