04OSGMQ

A.A. 2023/24

Course Language

Inglese

Course degree

1st degree and Bachelor-level of the Bologna process in Matematica Per L'Ingegneria - Torino

Course structure

Teaching | Hours |
---|

Teachers

Teacher | Status | SSD | h.Les | h.Ex | h.Lab | h.Tut | Years teaching |
---|

Teaching assistant

Context

SSD | CFU | Activities | Area context |
---|---|---|---|

SECS-S/01 | 6 | C - Affini o integrative | Attività formative affini o integrative |

2022/23

The course aims to provide the basic mathematical tools and formalism necessary to obtain a quantum description of physical systems, and to discuss their application in predicting quantum phenomena, effects and properties characterizing systems such as the hydrogen and helium atoms, elementary molecule and
matter-radiation models, the electromagnetic field, and systems of identical particles.

The course aims to provide the basic mathematical tools and formalism necessary to develop a quantum description of physical systems, and to discuss their application in predicting quantum phenomena, effects and properties characterizing systems such as the hydrogen and helium atoms, elementary molecule and matter-radiation models, the electromagnetic field, and systems of identical particles.

Students are expected 1) to achieve an effective understanding of the fundamental concepts and formal tools of Quantum Mechanics, 3) to develop ability in using them in the study of quantum systems, and 3) to develop a correct approach to the investigation of quantum systems.
These achievements are certainly important for subsequent courses such as solid-state and condensed-matter physics, field theory, quantum statistical mechanics, nuclear physics.

Students are expected 1) to achieve an effective understanding of the fundamental concepts and formal tools of Quantum Mechanics, 3) to develop ability in using them in the study of quantum systems, and 3) to develop a correct approach to the investigation of quantum systems.
These achievements are certainly important for subsequent courses such as solid-state and condensed-matter physics, field theory, quantum statistical mechanics, nuclear physics.

The knowledge of differential calculus, linear algebra concepts, vector-space theory and matrix diagonalization is required as well as the knowledge of the principles, laws and theorems of classical Mecahnics and electromagnetism.

The knowledge of differential calculus, linear algebra concepts, vector-space theory and matrix diagonalization is required as well as the knowledge of the principles, laws and theorems of classical Mecahnics and electromagnetism.

1) The Lagrangian and Hamiltonian approaches to classical mechanics. (0.5 cr)
2) The postulates of Quantum Theory. Time evolution of quantum systems. The Eherenfest theorem. The canonical-quantization scheme. (0.5 cr.)
3) The Hilbert space of quantum states. Scalar product, completeness relation. Properties of Hermitian operators and eigenvalue equations. (0.7 cr.)
4) Raising and lowering operators, solution of the harmonic-oscillator problem. The Heisenberg uncertainty relation. Coherent states and semiclassical picture of quantum systems. (0.6 cr).
5) Spectrum and eigenstates of the angular momentum. The two-body problem. The hydrogen atom. (1.0 cr.)
6) Dirac's formulation of quantum states and operators. The Schroedinger and Heisenberg representations of quantum Mechanics. (0.6 cr)
7) The spin operator and spin states. Addition of angular momenta. Time-independent perturbation theory. (0.7 cr)
8) Charged particles in the electromagnetic field. The Zeeman effect for Hydrogen atoms (weak and strong-field limit) (0.8 cr)
9) Symmetric and antisymmetric states of identical particles. Bosons, fermions and symmetrization principle. The exclusion principle. The Helium atom. (0.6 cr)

1) The Lagrangian and Hamiltonian approaches to classical mechanics. (0.5 cr)
2) The postulates of Quantum Theory. Time evolution of quantum systems. The Eherenfest theorem. The canonical-quantization scheme. (0.5 cr.)
3) The Hilbert space of quantum states. Scalar product, completeness relation. Properties of Hermitian operators and eigenvalue equations. (0.7 cr.)
4) Raising and lowering operators, solution of the harmonic-oscillator problem. The Heisenberg uncertainty relation. Coherent states and semiclassical picture of quantum systems. (0.6 cr).
5) Spectrum and eigenstates of the angular momentum. The two-body problem. The hydrogen atom. (1.0 cr.)
6) Dirac's formulation of quantum states and operators. The Schroedinger and Heisenberg representations of quantum Mechanics. (0.6 cr)
7) The spin operator and spin states. Addition of angular momenta. Time-independent perturbation theory. (0.7 cr)
8) Charged particles in the electromagnetic field. The Zeeman effect for Hydrogen atoms (weak and strong-field limit) (0.8 cr)
9) Symmetric and antisymmetric states of identical particles. Bosons, fermions and symmetrization principle. The exclusion principle. The Helium atom. (0.6 cr)

The teaching approach of this course is the traditional one based on frontal lectures. Each part of the program and the relevant calculations are discussed, step by step, and showed on the blackboard. As shown in the syllabus, the course is essentially divided in two sections: 1) Introduction to quantum physics, definition and/or derivation of the new formalism, methods and new theoretical tools necessary to develop the quantum-mechanical approach to physical systems, 2) study of various fundamental physical systems with the goal to achieve an effective modeling of such systems and to highlight their properties and significant effects. Exercise are proposed in the form of simple applications of the theory that each student must solve on his own. Solutions are provided in the subsequent lectures. Weekly meetings will be scheduled to give the students participting in this course the possibility to ask for questions, express doubts and clarify unclear points.

The teaching approach of this course is the traditional one based on frontal lectures. Each part of the program and the relevant calculations are discussed, step by step, and showed on the blackboard. As shown in the syllabus, the course is essentially divided in two sections: 1) Introduction to quantum physics, definition and/or derivation of the new formalism, methods and new theoretical tools necessary to develop the quantum-mechanical approach to physical systems, 2) study of various fundamental physical systems with the goal to achieve an effective modeling of such systems and to highlight their properties and significant effects. Exercise are proposed in the form of simple applications of the theory that each student must solve on his own. Solutions are provided in the subsequent lectures. Weekly meetings will be scheduled to give the students participting in this course the possibility to ask for questions, express doubts and clarify unclear points.

The PDF file containing the notes relevant to the course lectures are available in the web page of this course accessible through the Teaching Portal of Politecnico.
Franz Schwabl , Quantum Mechanics, Springer-Verlag 2007
David J. Griffiths, Introduction to Quantum Mechanics, Addison-Wesley 2005;

The PDF file containing the notes relevant to the course lectures are available in the web page of this course accessible through the Teaching Portal of Politecnico.
Franz Schwabl , Quantum Mechanics, Springer-Verlag 2007
David J. Griffiths, Introduction to Quantum Mechanics, Addison-Wesley 2005;

The exam is oral and consists of three questions concerning different topics of the course. Each question corresponds to a score of 10 out of 30 marks. The goal, in general, is to test the knowledge of the course program. These questions aim to evaluate the understanding of students concerning 1) the methodology
used to quantize classical systems, 2) the significant properties and effects that characterize physical systems as a consequence of the quantization process and 3) the mathematical tools used to develop quantum mechanics. To this end one of the three question is focused on proving/discussing some theorem or general property characterizing quantum systems and the mathematical formalism of quantum mechanics. The other questions are devoted to discuss the quantization of physical systems for some specific case and/or to determine quantum effects and physical properties of interest emerging from this process.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.

The exam is oral and consists of three questions concerning different topics of the course. Each question corresponds to a score of 10 out of 30 marks. The goal, in general, is to test the knowledge of the course program. These questions aim to evaluate the understanding of students concerning 1) the methodology
used to quantize classical systems, 2) the significant properties and effects that characterize physical systems as a consequence of the quantization process and 3) the mathematical tools used to develop quantum mechanics. To this end one of the three question is focused on proving/discussing some theorem or general property characterizing quantum systems and the mathematical formalism of quantum mechanics. The other questions are devoted to discuss the quantization of physical systems for some specific case and/or to determine quantum effects and physical properties of interest emerging from this process.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.

© Politecnico di Torino

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY