Learning objectives
This course offers the elements of Quantum Mechanics at the basis of the Physics of Atoms, Molecules and Nuclei. The required mathematical methods are developed, including partial differential equations, functional analysis and numerical analysis (elements of).
Prerequisites
Calculus, Classical Mechanics, elements of Electromagnetism and Waves
Course unit content
Wave properties of atomic particles, SCHROEDINGER Equation, simple examples in one dimension, three dimensional systems with spherical symmetry, Hydrogen atom, approximate methods for computing the spectrum, tunnel effect and potential scattering.
Full programme
Resumé of classical mechanics in the Hamiltonian formulation. Variational principles of Fermat and Maupertuis, analogy between geometrical optics and mechanics. Derivation of Schroedinger equation from the wave hypothesis of De Broglie and variational principles. Solution of Schroedinger equation for simple systems in one dimension and for central potentials. Hydrogen atom. Numerical approach for the calculation of the spectrum in up to 3 dimensions. Approximation methods: perturbation theory, Ritz variational method, WKB. The angular momentum in Quantum Mechanics. The role of symmetry. Tunnel effect and potential scattering (Born's integral equation and approximation).
Bibliography
Landau Lifshitz, Quantum Mechanics,
Dirac, Principles of Quantum Mechanics
Sakurai, Modern Quantum Mechanics
Teaching methods
Classroom lectures and problem solving
Assessment methods and criteria
Written and oral examination
Other information
The main emphasis is on wave mechanics, but some hints to Dirac's formulation and to Feynman's are provided.
