Quantum phisycs 1

A.Y. 2020/2021
Overall hours
Learning objectives
This course proivdes an introduction to the ideas and methods of quantum physics. In ths first part, the motivations for quantum physics are presented, its basic principles are introduced and the formalisim of non-relativistic quantum mechanics is developed, specifically in one dimension.
Expected learning outcomes
At the end of part 1 the student:
1. will be able to justify the need for a quantum description of Nature;
2. Will be able to construct the quantum operators associated to physical observables, to understand the probabilistic nature of the masurement of observables, and to classify (also using the density matrix formalism) the information content of a quantum state;
3. Will be able to quantize a one-dimensional mechanical system
4. Will be able to determine the time evolution of quantum systems, using the Heisenberg or the Schroedinger picture;
5. Will understand the properties of plane waves and wave packets;
6. Will be able to solve the Schroedinger equation with a variety of one-dimensional potentials (steps, wells, etc) which give rise to discrete or continuous spectra;
7. Will be able to determine the spectrum of the harmonic oscillator and will be able to manpulate creation and annihilation operators, also for the construction of cohernet states.
Course syllabus and organization


Lesson period
Second semester
Course syllabus
A. Critical revision of the formulation of classical mechanics
1. States, observables, time evolution in the canonical formulation
2. Extension necessary to cover the probabilistic description of Statistical Mechanics

B. Principles
1. Superposition principle
2. Observables and operators
3. Uncertainty

C. Canonical quantisation
1. Harmonic oscillator
2. Representations
3. Free particle

D. Temporal evolution
1. Hamiltonian
2. Schrödinger equation
3. Heisenberg equations

E. Semi-classical formulation
Prerequisites for admission
General physics, linear algebra, analysis
Teaching methods
The course consists of lectures (40 hours) and recitations (20 hours). All lectures are done on the blackboard and involve the presentation of theoretical and methodological arguments. The recitations are devoted to o the discussion of problem sets.
Teaching Resources

Dirac, P. A. M.
Landau, L.
Forte S., Rottoli
Sakurai, J. J.
Weinberg, S.
Galindo, Pascual
Destri, Onofri

Collections of problems and exercises:
E. d'Emilio, L. E. Picasso, Problemi di meccanica quantistica; ETS (elementari ed intermedi)
Assessment methods and Criteria
The exam at the end of part I is an intermediate three-hour long written test which requires solving a number of quantum physics problem of increasing degree of complexity, that cover the main topics of the syllabus.
Practicals: 24 hours
Lessons: 40 hours
Professor: Caracciolo Sergio


Lesson period
Second semester
If it is not possible to deliver the lectures in presence, they will be delivered telematically via the Zoom platform according to the same scheduled times. The lessons will be recorded and will remain available to students.

The written exam will be telematic with a susequent telematic oral exmination.
Course syllabus
A. Experimental facts at the roots of Quantum Mechanics
1. Waves and particles
2. Superposition, interference, measurement

B. Foundations
1. State vectors
2. Operators and observables
3. Indetermination
4. Information

C. Canonical quantisation
1. Coordinates representation
2. Momentum and translations
3. Canonical commutators

D. Time evolution
1. The time-evolution generator
2. The Schroedinger's equation
3. Heisenberg formulation

E. The free particle
1. Plane waves
2. Wave packets and states with minimal indetermination
3. Wave-packet motion

F. One-dimensional problems
1. Potential well and bound states
2. Step potential and scattering problems
3. Potential barrier and tunnelling effect.

G. The harmonic oscillator
1. Creation and destruction operators
2. Eigenfunctions and Schroedinger formulation
3. Time evolution and coherent states
Prerequisites for admission
Conoscenze di base di meccanica classica, analisi matematica ed algebra lineare.
Teaching methods
Theoretical lectures and explicit solution of problems, at the blackboard.
Teaching Resources
Recommended textbooks:
J.J. Sakurai, Modern Quantum Mechanics, Cambridge University Press.
L. E. Picasso, Lectures in Quantum Mechanics, Springer.
L.D. Landau, E.M. Lifšits, Quantum Mechanics: Non-Relativistic Theory, Pergamon.

Exercises with solutions:
E. d'Emilio, L. E. Picasso, Problems in Quantum Mechanics: With Solutions, Springer.
A. Z. Capri, Problems and Solutions in Nonrelativistic Quantum Mechanics, World Scientific.
K. Tamvakis, Problems and Solutions in Quantum Mechanics. Cambridge U.P..
Assessment methods and Criteria
- Written exam in presence with two tests, one at the end of the first part (Modulo 1) and one a the end of the second part (Modulo 2) (oral test not mandatory).
- Written exam in presence at the end of the second part (Modulo 2) (oral test not mandatory).
Practicals: 24 hours
Lessons: 40 hours