Quantum Phisycs 1
A.Y. 2024/2025
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
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
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 7
Practicals: 24 hours
Lessons: 40 hours
Lessons: 40 hours
Professors:
Ferrera Giancarlo, Röntsch Raoul Horst
CORSO B
Responsible
Lesson period
Second semester
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
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
Basic knowledge of classical mechanics, calculus and linear algebra
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..
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
Alternatively:
- Two written exams, 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).
- A single written exam at the end of the second part (Modulo 2) (oral test not mandatory).
- Two written exams, 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).
- A single written exam at the end of the second part (Modulo 2) (oral test not mandatory).
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 7
Practicals: 24 hours
Lessons: 40 hours
Lessons: 40 hours
Professors:
Archidiacono Maria, Zaro Marco
Professor(s)