# MODERN PHYSICS

OVERVIEW

The course describes the basic principles of quantum mechanics, its physical motivations, its mathematical formalisms, its main applications to atomic and molecular physics, to gases and condensed matter.

## AIMS AND CONTENT

LEARNING OUTCOMES

It is expected that the student will have a good knowledge of the main quantum phenomena in atoms, molecules, gas and solids.

AIMS AND LEARNING OUTCOMES

It is expected that the student will acquire a familiarity with the basic principles which characterize the quantum description of physical phenomena and an understanding of the physical contexts in which such description is required. It is also expected that he will learn to solve simple problems involving quantum particles or simple quantum mechanical systems.

Teaching methods

Traditional lectures for 70 hours.

SYLLABUS/CONTENT

The course, after an introduction about the early stages of the discovery of quantum theory and the description of the so-called old quantum theory, describes the formalism of modern quantum theory and the simplest applications of Schroedinger equation to atomic and molecular physics.

Detail syllabus:

- The crisis of classical physics: Rutherford atom. Photoelectric effect. Specific heats. Compton effect. Emission and absorption atomic spectra.

- The old quantum theory: Bohr-Sommerfeld quantization condition. De Broglie wave length. Wave-particle dualism.

- Mathematical foundations: Complex numbers, Matrices, Linear systems.

- The formalism of quantum mechanics: the superposition principle, states, vectors, operators and observables. Wave function in the Schrodinger representation. Spin systems.

- The Schrodinger equation and its applications: Continuous and discrete spectra. Potential wells. Tunnel effect. Harmonic oscillator. Periodic potentials and bands.

- The atom: Angular momentum. Hydrogen atom. The spin of the electron. Identical particles and the Pauli exclusion principle.

- Approximation methods: Stark effect. Zeeman effect. Helium atom. Molecules and chemical bonds.

RECOMMENDED READING/BIBLIOGRAPHY

-La fisica di Feynman*, Volume 3. “Meccanica quantistica” (Zanichelli* *2007); freely available on line in english**: http://www.feynmanlectures.info/*

- Lezioni di Meccanica Quantistica, L.E. Picasso, Edizioni ETS, (2000) Pisa;

**- **Chimica Fisica, Peter Atkins e Julio De Paula, (Zanichelli 2012);

**-** Introduction to Quantum Mechanics: S.M. Blinder (Elsevier, 2004).

- Introduction to Quantum Mechanics: David J. Griffiths (Benjamin Cumming, 2004);

- Modern Quantum Mechanics: J. J Sakurai (Addison Wesley, 1993);

- Lecture notes and problems collections available on-line: https://www.ge.infn.it/~imbimbo

## TEACHERS AND EXAM BOARD

Exam Board

PIERANTONIO ZANGHI' (President)

SILVANA TERRENI

PAOLO SOLINAS

NICODEMO MAGNOLI

NICOLA MAGGIORE

CAMILLO IMBIMBO

## LESSONS

Teaching methods

Traditional lectures for 70 hours.

## EXAMS

Exam description

Written test and oral exam.