# INTRODUCTION TO QUANTUM MECHANICS

## Learning outcomes of the course unit

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 contents summary

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.

## Course contents

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).

## Recommended readings

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 informations

The main emphasis is on wave mechanics, but some hints to Dirac's formulation and to Feynman's are provided.