Learning outcomes of the course unit
Knowledge of the princples of Qunatum Mechanics with attention to the chemical phenomena.
Course contents summary
Euclidean space and rectangular Cartesian coordinates. Rotations in E3. Linear operators in E3 . Algebra of rotations group. Transformation of a function under a rotation of the references axes. Translations group. Euclidean group. Space inversion.
FINITE DIMENSIONAL LINEAR SPACES : EN ANDCN'.
N-dimensional Euclidean space. N-dimensional complex linear space. Secular equation, eigenvectors and eigenvalues.
LINEAR VECTOR SPACES.
Definitions and general properties. Infinite dimensional linear spaces. Functions spaces.
HERMITIAN REPRESENTATIONS OF THE SO(3) ALGEBRA .
Introduction. Diffraction due to two point like holes. Diffraction due to a diaphragm. Davisson-Germer experiment of electron scattering by a Nickel crystal. Photoelectric effect. Photon polarization measurement. Conclusion.
Postulates of quantum measurement and of' quantum dynamics. Analysis of' postulate 5): Schroedinger picture and Heisenberg picture. Momentum operator. Uncertainty relations. Property of canonically conjugate operators and time role. Wigner theorem. Galilei group and ray representation. Parity transformation. Interaction.
SYNTHETICAL REVIEW OF CLASSICAL ELECTROMAGNETISM
GAUGE TRANSFORMATIONS .AND QUANTUM MECHANICS
Introduction. Electromagnetic field equations. Electrostatic and magnetostatic fields. Fields generated by non stationary charge and current densities. Choice of gauge. Galilean non invariance. Transversal electromagnetic waves. Polarization of electromagnetic waves generated by sources. Local phase transformation and gauge transformation.
HAMILTONIAN SIMMETRY AND HILBERT SPACE.
SYSTEM OF MANY IDENTICAL PARTICLES.
Postulate 6): symmetryzation principle. Hamiltonian of a system of many identical charged particles. identical particles when the symmetryzation postulate is neglected - S2 group. Properties of the Hamiltonian and its eigenvectors for a system of N identical particles when the symmetryzation postulate is neglected SN group.
Irreducible representations of SN..
METHODS OF APPROXIMATE SOLUTIONS.
Introduction. Time independent perturbation and non degenerate spectrum. Method of Rayleigh-Schroedinger. Time independent perturbation and degenerate spectrum. Method of Rayleigh-Sohroedinger. Time dependent perturbation. Variational method of Ritz.
RADIAL MOMENTUM - MOMENTUM AND ANGULAR MOMENTUM IN POLAR COORDINATES
Introduction. Radial momentum and angular momentum. Angular Momentum in polar coordinates and spherical harmonics.
ADDITION OF ANGULAR MOMENTA AND CLEBSCH-GORDON COEFFICIENTS.
Classical solution. Quantum solution.
Introduction. One-dimensional quantum harmonic oscillator. Three dimensional isotropic harmonic oscillator and unitary symmetries.
ABSORPTION AND INDUCED EMISSION - SEMICLASSICAL RADIATION THEORY.
Hamiltonian of an atomic system and its symmetry. Central field approximation. Atomic spectral terms classification in the central field approximation. Hartree-Fook equations and self-consistent field solution. Table of the atomic elements.
M. Hamermesh, Group theory, Addison-Wesley
P.M.A. Dirac, The principles of Quantum Mechanics, Oxford University Press
H. Eyring, J. Walter, G. Kimball, Quantum Chemistry, Wiley