Acquisition of the basic concepts of quantum theory (wave function, Schrodinger equation, quantization of energy levels, etc.) and their utilization in the description of atoms and molecules.
Expected learning outcomes
The student will be able to understand the physical meaning and the conditions of applicability of the laws and theorems at the base of Quantum Chemistry, applying them to the resolution of simple problems
Lesson period: First semester
(In case of multiple editions, please check the period, as it may vary)
The Dawn of Quantum Theory: Blackbody Radiation, Photoelectric Effect, Vibration of Atoms in Crystals, Hydrogen Atomic Spectrum, De Broglie Waves, Uncertainty Principle. The Classical Wave Equation: One- imensional W. E., Separation of Variables, Superposition of Normal Modes, Vibrating Membrane. The Schroedinger Equation: Linear Operators, Eigenvalue Problems, Interpretation of the Wave Function, Average Quantities, Particle in a Box, Tunneling. The Postulates of Quantum Mechanics: State Functions, Observable Quantities and Eigenvalues, Commutators, Hermitian Operators, Commutating Operators, Time Dependent Schroedinger Equation. The Harmonic Oscillator: Energy Levels and Wave Functions, Hermite Polynomials, H.O. as a Model of a Diatomic Molecule. The Rigid Rotator: Energy Levels and Spherical Harmonics. The Hydrogen Atom: Energy Levels and Orbitals. Techniques of approximation: Time-independent pertrubation theory. Variation theory. The Hellmann-Feynman theorem. Time-dependent perturbation theory. WKB. The structure of helium. Many-electrons atoms. Thomas-Fermi and Thomas-Fermi-Dirac method. Introduction to molecular electronic structure theory. The Born-Oppenheimer approximation. Molecular orbital theory. The Hartree-Fock and the self-consistent field method. Post Hartree-Fock methods. The electronic correlation. The dneisty function theory (DFT).
Prerequisites for admission
Basic knowledge of math, physics and chemical physics acquired during the first years of bachelor courses either in chemistry or industrial chemistry.
The course will be taught either using the blackboard or electronic slides. The course will be taught in Italian. The student is warmly advised to attend the lessons.
- D.A. McQuarrie, Quantum chemistry, 2nd ed., University Science Books, USA, 2008 - P. Atkins and R. Friedman, Molecular Quantum Mechanics, Oxford University Press.
Assessement methods and criteria
The examination consists of an oral interview or written test, roughly 40' long. The student will be asked to reproduce the physical proofs of theorems shown during the classroom lectures. To this end, the student will be prompted to solve simple exercises under the instructors' supervision on topics treated during the lessons.