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 the student will be able to

1. apply the Schrödinger equation to interacting (possibly identical) two-particle systems 

2. 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 compose angular momenta

5. relate the laws of motion of classical mechanics to those of

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

6. 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. express the cross section in terms of a transition amplitude

9. write the wave function for a system of identical particles 

10. 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 teacher

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

FISICA QUANTISTICA B:

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

Exam Board

CAMILLO IMBIMBO (President)

STEFANO GIUSTO

SIMONE MARZANI

NICOLA MAGGIORE (President Substitute)

LESSONS

Class schedule

The timetable for this course is available here: Portale EasyAcademy

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