
Quantum Physics
Code: 107633Credits: 6
| Degree programme | Type | Course |
|---|---|---|
| Physics | OB | 2 |
Contact lecturer
- Name :
- Gabriele De Chiara
- Email :
- gabriele.dechiara@uab.cat
Teaching staff
- Jordi Romero i Pallejà
- Javier Lalueza Puertolas
- Guillermo Abad López
- Albert Aloy Lopez
- Gabriele De Chiara
- Ramón Muñoz Tapia
Group languages
You can consult this information at the end of the document.
Prerequisites
It is recommended that students start Quantum Physics meeting a few reasonable prerequisites. One has to take into account that quantum physics is one of the most difficult subjects in physics, either because of its anti-intuitive and very broad content (it affects many parts of physics), or because it involves several sophisticated mathematical tools:
Physics: Knowledge of classical mechanics including, at an elementary level, Hamiltonian formulism; Knowledge of electromagnetism, waves and first-year optics
Mathematics: knowledge of algebra, including vector spaces (with metrics), linear operators and eigenvectors and eigenvalues; elementary knowledge of complex numbers, integration of functions of several variables, and differential equations.
General: it takes an open mind and an ability (training) to keep up with the course work that involves formal and conceptual difficulties.
Objectives
The aim is to introduce students to the world of quantum mechanics, which is an essential part of modern physics. To expose them and to help them reach the fundamental concepts and the basic formalism of this discipline. Illustrate its usefulness, importance and meaning with applications. To provide a training to tudents that will allow them to deepen and broaden their knowledge in Quantum Physics II and in the optional subjects of Quantum Mechanics, Advanced Quantum Mechanics, Quantum Information, Quantum Optics, among others.
The (no-exhaustive) list of basic objectives is:
(i) Know the experiments that gave birth to quantum mechanics
(ii) Identify the quantum formulation and postulates in finite and infinite dimensional systems.
(iii) Make temporal evolutions in spaces of finite dimension (essentially dimension 2)
(iv) Know the wave formulation in space of coordinates and moments
(v) Solve the energy spectrum and states of simple 1D potentials (wells and harmonic oscillator) in wave mechanics
(vi) Description of collision states (scattering) in simple potential barriers and know the differences with bound states
(vii) Knowing how to make the temporal evolution of a free wave packet.
(viii) Solve simple problems in 3D (infinite well and isotropic and non-isotropic harmonic oscillator). Analyze degeneracies.
(ix) Sovle problems with radial symmetry, Laplacian expressions and orbital angular momentum.
(x) Solve the spectrum of the hydrogen atom
Learning outcomes
- CM28 (Solve problems in the field of quantum physics accurately, using approximations and applying the knowledge of quantum theory in the professional field.) Solve problems in the field of quantum physics accurately, using approximations and applying the knowledge of quantum theory in the professional field.
- CM29 (Identify the applications of quantum mechanics and their technological and social impact in the professional field.) Identify the applications of quantum mechanics and their technological and social impact in the professional field.
- KM32 (State the principles of quantum mechanics and their application in the description in various dimensions of paradigmatic physical systems of one or more bodies.) State the principles of quantum mechanics and their application in the description in various dimensions of paradigmatic physical systems of one or more bodies.
- KM33 (Identify the quantum description of fields and symmetries, both discrete and continuous.) Identify the quantum description of fields and symmetries, both discrete and continuous.
- KM34 (Describe applications of quantum mechanics in quantum communications, computing, and simulation.) Describe applications of quantum mechanics in quantum communications, computing, and simulation.
- SM26 (Mathematically solve problems related to paradigmatic quantum systems.) Mathematically solve problems related to paradigmatic quantum systems.
- SM27 (Apply the main techniques of quantum mechanics in the identification of the atomic structure of single atoms.) Apply the main techniques of quantum mechanics in the identification of the atomic structure of single atoms.
Contents
Physical grounds of Quantum Physics. Experimental facts and basic consequences. Indeterminations and Heisenberg principle.
Basic formulism of the Quantum Physics. States and observables. Vector spaces. Operators. Dirac Notation.
Postulates of Quantum Physics. Matrix mechanics (Heisenberg) and wave mechanics (Schrödinger).
One dimensional applications of wave mechanics: simple potential wells, tunnel effect, harmonic oscillator, diatomic molecules.
Three-dimensional applications of wave mechanics: orbital angular momentum and spherical harmonics, hydrogen atom. Central potentials.
Learning activities and methodology
| Title | Hours | ECTS | Learning outcomes |
|---|---|---|---|
| Study theory | 40 | 1.6 | |
| Exercise sessions (problem solving and seminars) | 22 | 0.88 | |
| Solve assigned problems | 51 | 2.04 | |
| Theory lectures | 28 | 1.12 |
Theory lectures: In the theory classes we introduce the key concepts and methods that define the contents of the subject. Before each class the students must become familiar with the subject, making us of the material (notes, videos or bibliography) that will be made available to them.
Problem sessions: The exercises illustrate the application of the concepts learned to specific problems of pedagogical or practical relevance. They should also serve the student to strengthen her or his mathematical skills.
A part of the problems are solved in class by the teacher, so that the students -who will have previously attempted to solve the problems at home- can know the degree of success of their solutions and incorporate the pertinent corrections; other problems must be solved and delivered by the student directly to the teacher. The CV contains several tests to help the student to assess his/her degree of comprehension of the course.
There are four scheduled sessions of 2 hours each, where problems will be done in groups of 3-4 randomly assigned students. These problems will address some aspects in a more exhaustive way and allow to illustrate the application of concepts in more depth as well as learning some new techniques.
Tutoring: The individual tutorials (eventually, it will be possible to organize some in groups) can be used to solve any issues or difficulties.
Home activities:
Study and preparation of Theory classes.
Study and resolution of problems.
Peer reviewing of projects
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| First evaluation | 40-45% redeemable | 3 | 0.12 | CM28, KM32, KM33, SM26, SM27 |
| Make up exam | 100% | 3 | 0.12 | CM28, KM32, KM33, SM26, SM27 |
| Assignment i and problem Sessions | 10-20% | 0 | 0 | CM28, CM29, KM32, KM34, SM26 |
| Second evaluation | 42.5-45% redeemable | 3 | 0.12 | CM28, KM32, KM33, SM26, SM27 |
Evaluation
All assessments will be conducted in writing. Each examination will consist of two sections, Theory and Problems, which will have equal weight. No supporting materials may be used during the examinations, except for a mathematical formula sheet, which will either be provided with the exam or prepared in advance by the student.
The first assessment (Theory and Problems) will take place after approximately seven weeks of teaching and will cover roughly half of the course syllabus. The second assessment will be held approximately seven weeks later and will cover the remaining half of the syllabus.
Both the first and second partial examinations may be retaken at the end of the semester through a final assessment (resit examination), which also provides an opportunity to improve previously obtained grades. In other words, there will be two partial examinations and, for students who require or wish to do so, a resit examination covering the relevant parts of the course. A minimum grade of 3.0 must be obtained in each part. As a general rule, students must have sat both partial examinations to be eligible for the resit examination, although special circumstances may be considered.
Assignments and problem-session activities may contribute up to two points to the grades obtained in the partial examinations. These points do not apply to the final recovery examination grade.
A student will be considered assessable if they submit any of the partial or final examinations.
For students who have already passed one or more partial examinations and choose to retake them in order to improve their grade, the following rule will apply: if the resit grade is higher than the original grade, the resit grade will replace the original grade. If the resit grade is lower, the final grade will be calculated as a weighted average consisting of 75% of the original grade and 25% of the resit grade.
Single assessment
Students who opt for the single assessment modality must complete a final assessment consisting of: (i) a theory exam covering the entire course content; (ii) a problem-solving exam consisting of exercises similar to those carried out in the Classroom Practice sessions; and (iii) upon completion of these exams, an oral assessment on concepts developed during the seminar sessions.
All components of the assessment will take place on the same day, at the same time, and in the same location as the second-part assessments of the continuous assessment modality.
The final grade will be calculated as the weighted average of the three assessment components: the theory exam will account for 40% of the final grade, the problem-solving exam for 40%, and the oral assessment for 20%. Students who do not obtain a final grade of at least 5.0 will have a further opportunity to pass the course through the resit examination, which will generally be held on the official resit date or on a date established by the degree coordinator. In the resit examination, up to 70% of the grade corresponding to the theory and problem-solving components may be recovered. The oral assessment component is not recoverable.
Note
Any irregularity committed in an assessment activity (academic fraud, plagiarism, or improper use of AI, unless such use is expressly authorized in the course syllabus) that may lead to a significant alteration of the grade will result in that assessment activity being graded with a 0. If the course syllabus stipulates that obtaining a minimum grade in that assessment activity is an essential requirement for passing the course, or if multiple irregularities occur in assessment activities within the same course, the final grade for the course will be 0. Furthermore, disciplinary proceedings may be initiated against any student who commits any of these irregularities.
Bibliography
Basic
F. Mandl, ``Quantum Mechanics'', John Wiley 1992. Llibre de referència que tradicionalment s'ha fet servir a Física Quàntica la UAB i del que disposeu moltes copies a la Bilbioteca de Ciències. S'hi troben molts continguts del curs, tot i així trobareu una exposició més moderna (i pel meu gust més clara) al Griffiths i Ballentine.
D. J. Griffiths, “Introduction to Quantum Mechanics”, Pearson Prentice Hall; 2nd Ed. 2004.
Advanced
L. Ballentine, ``Quantum Mechanics: A Modern Development'', World Scientific Publishing Company, 1998.
J. J. Sakurai, ``Modern Quantum Mechanics'', Addison Wesley, 1993.
C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics vol.1-2, Wiley-Interscience, 2006.
A. Galindo y P. Pascual, \" Mecánica Cuántica\", Vol. I,II y III, Eudema Universidad, Madrid 1989. (there is also an English edition)
Other
Eisberg, Resnick. Física Cuántica. Átomos, Moléculas, Sólidos, Núcleos y Partículas. 2002 (original edition in english)
Alonso, Marcelo, and Edward J. Finn. \"Fisica\" Vol III: Fundamentos cuanticos y estadisticos\". Ed. Rev. Addison Wesley Longman, 2000.(original edition in english)
Software
No specific programs are necessary for the course, but access to the programs Mapple or Mathematica may be convenient to check and extend some results. The LaTeX word processor is very useful for the presentation of the deliverables.
Course groups and languages
The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE
| Type of teaching | Group | Language | Semester | Shift |
|---|---|---|---|---|
| (TE) Theory | 1 | Catalan | second semester | morning-mixed |
| (PAUL) Classroom practices | 1 | Catalan | second semester | morning-mixed |
| (TE) Theory | 2 | Catalan | second semester | morning-mixed |
| (PAUL) Classroom practices | 2 | Catalan | second semester | morning-mixed |
| (PAUL) Classroom practices | 3 | Catalan | second semester | morning-mixed |
| (SEM) Seminars | 11 | Catalan | second semester | morning-mixed |
| (SEM) Seminars | 12 | Catalan | second semester | morning-mixed |
| (SEM) Seminars | 21 | Catalan | second semester | morning-mixed |
| (SEM) Seminars | 22 | Catalan | second semester | morning-mixed |
| (SEM) Seminars | 31 | Catalan | second semester | morning-mixed |
| (SEM) Seminars | 32 | Catalan | second semester | morning-mixed |
| (TE) Theory | 70 | Catalan | second semester | morning-mixed |