RELATIVITY AND QUANTUM MECHANICS
RELATIVITÀ E MECCANICA QUANTISTICA
| A.Y. | Credits |
|---|---|
| 2025/2026 | 6 |
| Lecturer | Office hours for students | |
|---|---|---|
| Catia Grimani | Friday 4-6 pm: Teacher's office Section of Physics, Via. S. Chiara, 27 by appointment |
| Teaching in foreign languages |
|---|
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Course with optional materials in a foreign language
English
This course is entirely taught in Italian. Study materials can be provided in the foreign language and the final exam can be taken in the foreign language. |
Assigned to the Degree Course
| Date | Time | Classroom / Location |
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| Date | Time | Classroom / Location |
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Learning Objectives
The aim of this course is to provide insights on scientific discoveries and theories developed in the 1800s and in the 1900s especially Relativity and Quantum Mechanics.
Program
01. Introduction
01.01 Differential operators: nabla, gradient, divergence, rotor
01.02 Tensors
01.03 Maxwell equations in integral and differential form.
02. Modern Physics
02.01 Discovery of radioactivity
02.02 Discovery of the electron
02.03 Black body law and Planck's hypothesis
02.04 Photoelectric effect
02.05 X-rays
02.06 X-ray diffraction
02.07 Compton effect
02.08 Structure of the atom
03. Special relativity
03.01 Postulates of special relativity
03.02 Time dilation
03.03 Doppler effect for light
03.04 Length contraction
03.05 Lorentz transformations
03.06 Minkowski space-time
03.07 Relativistic invariance of Maxwell's equations
04 General relativity
04.01 The equivalence principle and general relativity
04.02 The metric tensor
04.03 The Ricci tensor
04.04 The energy-momentum tensor
04.05 The cosmological constant
04.06 Einstein's field equation
04.07 Gravitational waves
05. Quantum mechanics
05.01 Particles and waves
05.02 De Broglie waves
05.03 Energy of elementary particles and photons
05.04 Atomic spectra
05.05 Energy levels and spectra
05.06 Wave equations
05.07 Schroedinger equation
05.08 Confined particles
05.09 Heisenberg uncertainty principle
05.10 Reflection transmission from a potential barrier
05.11 Tunnelling effect
05.12 Harmonic oscillator
05.13 Schroedinger equation for the hydrogen atom
05.14 Quantum numbers
05.15 Zeeman effect
05.16 Spin
05.17 Total angular momentum
05.18 LS coupling
Bridging Courses
There are no mandatory prerequisites for this exam.
Learning Achievements (Dublin Descriptors)
Knowledge and understanding
At the end of this course, each student will know to understand and solve problems of Modern Physics of average difficulty as required by the number of teaching hours
Applying knowledge and understanding
At the end of the course the students will be able to apply the laws of Modern Physics to simple problems of Quantum Mechanics and Relativity
Making judgements:
The students will be able to apply their knowledge to problems not discussed during the teaching hours.
Communication skills:
Each student is more than recommended to ask questions during this course and to participate to discussions in order to improve his/her ability to present his/her work
At the end of the course the students will be able to present and discuss problems of Modern Physics with proper language and mathematical formalism required by the topics.
Teaching Material
The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it
Supporting Activities
The teaching material related to the supporting activities prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it
Teaching, Attendance, Course Books and Assessment
- Teaching
Theoretical lessons and applications.
Teaching is delivered in a mixed mode, that is, lessons are held in the classroom and are simultaneously transmitted remotely within the Moodle platform.
There are no intermediate tests. The assessment tests are the same for attending and non-attending students.
- Attendance
Although recommended, the course attendance is not mandatory.
- Course books
Arthur Beiser, "Concepts of Modern Physics", International Student Edition, Singapore, 1984
Cesare Rossetti, "Rudimenti di Meccanica Quantistica", Levrotto & Bella editori, 2011.
Robert Resnick, "Introduzione alla relatività ristretta", Casa editrice Ambrosiana, Milano, 1983 Capitolo sesto: Relatività ed elettromagnetismo
Bernard Schutz, "A first course in general relativity", Cambridge University Press, 2022
- Assessment
Oral test.
The oral test consists of three questions (theoretical questions or exercises) on different topics of the program. To each question/excercise is given a mark from 0 to 10 for a maximum of 30/30. Therefore, the exam is graded out of thirty and will be passed with a minimum mark of 18/30.
About oral interviews to assess the student's knowledge of the discipline we will evaluate:
Knowledge of concepts:
roughly describes the concepts and has poor understanding of them (insufficient)
describes the concepts acceptably and has an acceptable understanding of them (sufficient)
describes the concepts precisely and has a good understanding of them (good)
perfectly describes the concepts and has a full understanding of them (excellent)Technique applications and methods:
has a rough understanding of techniques for applications to case studies (insufficient)
has an acceptable knowledge of the techniques and an acceptable application skills (sufficient)
has a good knowledge of techniques and good application skills (good)
has an excellent knowledge of the techniques and an excellent ability to apply (excellent)Mastery of scientific language:
uses a common, non-scientific language (insufficient)
demonstrates limited language properties. Use of only a few specific terms (sufficient)
demonstrates good expression skills and uses a good number of specific terms (good)
demonstrates excellent language skills (excellent).
- Disability and Specific Learning Disorders (SLD)
Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.
To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.
Additional Information for Non-Attending Students
- Teaching
Same as for attending students
- Attendance
Same as for attending students
- Course books
Same as attending students
- Assessment
Same as for attending students
- Disability and Specific Learning Disorders (SLD)
Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.
To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.
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