Quantum Phisycs 1
A.Y. 2025/2026
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.
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.
Lesson period: Second semester
Assessment methods: Esame alla fine del gruppo
Assessment result: Inserire codice AF
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
CORSO A
Responsible
Lesson period
Second semester
Course syllabus
A. The experimental foundations of quantum physics
1. Waves and particles
2.Superposition, interference, measurement
B.Foundations
1.State vectors
2.Operators and observables
3.Uncertainty
4.Information
C. Canonical quantization
1.The coordinate basis
2. Momentum translations
3.The canonical commutator
D. Time evolution
1.The generator of time translations
2.The Schrödinger equation
3. The Heisenberg formulation of quantum mechanics
E. The free particle
1.Plane waves
2.Wave packets and minimum uncertainty
3.The motion of a wave packet
F. One-dimensional problems
1.The potential well and bound states
2.Scattering: the potential step
3.The potential barrier and tunneling
5. The harmonic oscillator
1.Spectrum and creation and annihilation operators
2. Eigenfunctions and the Schrödinger approach
3. Time evolution and coherent states
1. Waves and particles
2.Superposition, interference, measurement
B.Foundations
1.State vectors
2.Operators and observables
3.Uncertainty
4.Information
C. Canonical quantization
1.The coordinate basis
2. Momentum translations
3.The canonical commutator
D. Time evolution
1.The generator of time translations
2.The Schrödinger equation
3. The Heisenberg formulation of quantum mechanics
E. The free particle
1.Plane waves
2.Wave packets and minimum uncertainty
3.The motion of a wave packet
F. One-dimensional problems
1.The potential well and bound states
2.Scattering: the potential step
3.The potential barrier and tunneling
5. The harmonic oscillator
1.Spectrum and creation and annihilation operators
2. Eigenfunctions and the Schrödinger approach
3. Time evolution and coherent states
Prerequisites for admission
Calculus of one variable; linear algebra; waves and oscillations.
Teaching methods
The course consists of lectures (40 hours) and recitations (24 hours). All lectures are done on the blackboard and involve the presentation of theoretical and methodological arguments. Of the recitations, 10 hours are devoted to explaining standard applications, while 14 hours are devoted to the discussion of problem sets that have been assigned at the end of each lecture, directly involving students in the solution. The lecture record and all problems (with solution hints) are published on the instructors' website along the way.
Teaching Resources
Reference textbook
Stefano Forte, Luca Rottoli, Fisica Quantistica; Zanichelli. (in Italian)
Further reading
A. Berera e L. Del Debbio, Quantum Mechanics; Cambridge U.P. (useful for explicit computations)
B. Schumacher, M. Westmoreland, Quantum Processes, Systems & Information, Cambridge U.P. (useful mostly for general quantum theory other than mechanics)
S. Weinberg, Lectures on Quantum Mechanics; Cambridge U.P. (perturbation theory and scattering theory)
K. Gottfried e T.M. Yan, Quantum Mechanics: Fundamentals; Springer (more extensive treatment of several topics)
J. Binney e D. Skinner, The Physics of Quantum Mechanics; Oxford U.P. (more extensive treatment of several topics)
M. Longair, Quantum Concepts in Physics; Cambridge U.P. (historical sources with comment)
Collections of problems and exercises
G. Passatore, Problemi di meccanica quantistica elementare; Franco Angeli (elementary)
L. Angelini, Meccanica quantistica: problemi scelti; Springer (elementary)
E. d'Emilio, L. E. Picasso, Problemi di meccanica quantistica; ETS (elementary and intermediate)
A. Z. Capri, Problems and Solutions in Nonrelativistic Quantum Mechanics; World Scientific (elementary, intermediate and advanced)
K. Tamvakis, Problems and Solutions in Quantum Mechanics; Cambridge U.P. (intermediate and advanced)
V. Galitski, B. Karnakov, V. Kogan e V. Galitski, Exploring Quantum Mechanics; Oxford U.P. (700 problems, mostly intermediate and advanced)
Stefano Forte, Luca Rottoli, Fisica Quantistica; Zanichelli. (in Italian)
Further reading
A. Berera e L. Del Debbio, Quantum Mechanics; Cambridge U.P. (useful for explicit computations)
B. Schumacher, M. Westmoreland, Quantum Processes, Systems & Information, Cambridge U.P. (useful mostly for general quantum theory other than mechanics)
S. Weinberg, Lectures on Quantum Mechanics; Cambridge U.P. (perturbation theory and scattering theory)
K. Gottfried e T.M. Yan, Quantum Mechanics: Fundamentals; Springer (more extensive treatment of several topics)
J. Binney e D. Skinner, The Physics of Quantum Mechanics; Oxford U.P. (more extensive treatment of several topics)
M. Longair, Quantum Concepts in Physics; Cambridge U.P. (historical sources with comment)
Collections of problems and exercises
G. Passatore, Problemi di meccanica quantistica elementare; Franco Angeli (elementary)
L. Angelini, Meccanica quantistica: problemi scelti; Springer (elementary)
E. d'Emilio, L. E. Picasso, Problemi di meccanica quantistica; ETS (elementary and intermediate)
A. Z. Capri, Problems and Solutions in Nonrelativistic Quantum Mechanics; World Scientific (elementary, intermediate and advanced)
K. Tamvakis, Problems and Solutions in Quantum Mechanics; Cambridge U.P. (intermediate and advanced)
V. Galitski, B. Karnakov, V. Kogan e V. Galitski, Exploring Quantum Mechanics; Oxford U.P. (700 problems, mostly intermediate and advanced)
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 problems of increasing degree of complexity, that cover the main topics of the syllabus, and answering a simple theory question. All written tests of the last several years available from the instructors' website. The final grade is the weighted average of the grades obtained in the intermediate test (at the end of quantum physics I)
and in the final exam. In grading the written exam a particular weight is given to the check of understanding of basic principles.
and in the final exam. In grading the written exam a particular weight is given to the check of understanding of basic principles.
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 7
Practicals: 24 hours
Lessons: 40 hours
Lessons: 40 hours
Professor:
Forte Stefano
CORSO B
Responsible
Lesson period
Second semester
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 7
Practicals: 24 hours
Lessons: 40 hours
Lessons: 40 hours
Professor:
Vicini Alessandro
Professor(s)