Quantum phisycs 1

A.Y. 2021/2022
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
In case in-presence teaching is not possible, lectures will be held remotely using zoom, at the scheduled time. The zoom link will be madeavailable on the course website. Recordings of all lectures will be made available from the course website. A google group will be available for discussions among students and with the course teaching assistants and instructors.
Course syllabus
A. The experimental foundations of quantum physics

1. Waves and particles
2.Superposition, interference, measurement

1.State vectors
2.Operators and observables

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 which 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. A teaching assistant will be available and will take care of extra exercise sessions including a simulation of the written test.
Teaching Resources

Stefano Forte e Luca Rottoli, Fisica Quantistica; Zanichelli.

Recommended books
J.J. Sakurai, Modern Quantum Mechanics , Pearson (general reference)
F. Schwabl, Quantum Mechanics; Springer (useful for explicit computations)
S. Weinberg, Lectures on Quantum Mechanics; Cambridge U.P. (for deepening and special topics)
K. Gottfried e T.M. Yan, Quantum Mechanics: Fundamentals; Springer (for deepening and special topics)
J. Binney e D. Skinner, The Physics of Quantum Mechanics; Oxford U.P. (for deepening and special topics)

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 avanced)
K. Tamvakis, Problems and Solutions in Quantum Mechanics; Cambridge U.P. (intermediate and avanced)
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 problem 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.
Practicals: 24 hours
Lessons: 40 hours


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.
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
Basics of classical mechanics, calculus and linear algebra.
Teaching methods
Theoretical lectures and explicit solution of problems, in the classroom 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.
Assessment methods and Criteria
Written exam with two tests, at the end of the first and the second modules.
Practicals: 24 hours
Lessons: 40 hours
Professor: Vicini Alessandro
every day after 12.30
Physics department, room DC/I/6
Mo-Fr, after 2.30pm
To be agreed (email)
DC/1/6, Physics Department