**PHYSICS 8758 (coorte 2018/2019)**- ANALYTICAL MECHANICS 25911
- PHYSICS II 57049
- GENERAL PHYSICS 3 57050

## OVERVIEW

The phenomenological basis and the formal construction of non relativistic quantum mechanics are illustrated. The aim is to enable the student to solve simple quantum mechanics problems. The second part of the course is dedicated to applications (such as time evolution, approximation methods, scattering theory)

## AIMS AND CONTENT

LEARNING OUTCOMES

The course concerns the basic concepts of quantum mechanics, introduced in the module of Quantum Physics A, studying their application to three-dimensional systems, in particular the hydrogen atom, and introducing several formal developments, including the study of mixed states, perturbation theory, variational method, WKB method and scattering theory.

AIMS AND LEARNING OUTCOMES

At the end of these courses (A and B) the student

1. will be able to apply the Schrödinger equation for interacting (possibly identical) two-particle systems by means of a potential

2. will be able to determine the spectrum of the Hamiltonian for central problems through the use of spherical coordinates

3. determine the spectrum of the hydrogen atom

4. determine the spectrum of angular momentum operators (orbital and intrinsic (spin))

and will be able to compose angular moments

5. will know how to relate the laws of motion of classical mechanics to those of

quantum mechanics, using both the WKB method, and the variational method

6. will be able to calculate the time-independent perturbation to the spectrum of a known Hamiltonian

7. determine a transition amplitude by the theory of time-dependent perturbations

8. will know how to express the cross section in terms of a transition amplitude

9. will be able to write the wave function for a system of identical particles

10. will be able to determine the density matrix for a given statistical mixture and use it to calculate an average value

PREREQUISITES

Nonrelativistic quantum mechanics in one dimension (modulo A). Basic knowledge of classical mechanics and analytical mechanics, mathematical analysis, geometry and linear algebra.

TEACHING METHODS

The course is given by means of lectures that include:

• blackboard lessons

• blackboard exercises given by the professors

SYLLABUS/CONTENT

FISICA QUANTISTICA B:

1 Recalls of the formalism of quantum mechanics.

2 Unitary transformations. Symmetries in QM: translations and rotations.

Discrete symmetries: P, T. Mixed states and density matrix.

3 Hamiltonian of a charged particle in an electromagnetic field

4 Theory of time-independent perturbations. Fine structure of the

hydrogen atom, Zeeman effect, hyperfine structure.

5 Variational method. Ground state of the hydrogen atom,

hydrogen ion molecule.

6 The semiclassical approximation and the WKB method.

7 Theory of time-dependent perturbations. Representation

interaction. Fermi’s golden rule, density of states for

free particle. stimulated and spontaneous emission,

radiation absorption, meann lifetime of an excited state,

selection rules.

8 Scattering theory: Lippmann Schwinger equation,

Born approximation, Born series for the scattering amplitude, Green function as a propagator, partial waves expansion, phase shifts, S- matrix, unitarity condition,

optical theorem, low-energy scattering, scattering of identical

identical.

RECOMMENDED READING/BIBLIOGRAPHY

D. J. Griffith, Introduction to Quantum Mechanics, ed. Pearson

J. J. Sakurai, J. Napolitano, Modern Quantum Mechanics, ed. Pearson

L.D. Landau, E.M. Lifsits, vol. 3: Meccanica quantistica, Editori Riuniti

K.Konishi, G.Paffuti Quantum Mechanics: A New Introduction, ed. Oxford

## TEACHERS AND EXAM BOARD

**Office hours:** The reception time is free, by prior telephone or email appointment.
Dipartimento di Fisica, via Dodecaneso 33, 16146 Genova
piano 7, studio 709
telefono: 010 3536406
email: nicola.maggiore@ge.infn.it

**Office hours:** Please fix an appointment by e-mail.

Exam Board

CAMILLO IMBIMBO (President)

STEFANO GIUSTO

SIMONE MARZANI

NICOLA MAGGIORE (President Substitute)

## LESSONS

TEACHING METHODS

The course is given by means of lectures that include:

• blackboard lessons

• blackboard exercises given by the professors

Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

EXAM DESCRIPTION

written and oral exam

ASSESSMENT METHODS

The student is admitted to the oral exam if the written exam is passed according to the criteria described on aulaweb

Exam schedule

Date | Time | Location | Type | Notes |
---|---|---|---|---|

07/01/2021 | 14:00 | GENOVA | Scritto | |

03/02/2021 | 14:00 | GENOVA | Scritto | |

10/06/2021 | 14:00 | GENOVA | Scritto | |

05/07/2021 | 14:00 | GENOVA | Scritto | |

10/09/2021 | 14:00 | GENOVA | Scritto |