
Quantum physics I
Code: 100154Credits: 6
| Degree programme | Type | Course |
|---|---|---|
| Physics | OB | 3 |
Contact lecturer
- Name :
- Ramón Muñoz Tapia
- Email :
- ramon.munoz@uab.cat
Teaching staff
- Gabriele De Chiara
- Arnau Diebra Huertas
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) Know 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) Solve problems with radial symmetry, Laplacian expressions and orbital angular momentum.
(x) Solve the spectrum of the hydrogen atom
Learning outcomes
- Use critical reasoning, show analytical skills, correctly use technical language and develop logical arguments
- Transmit, orally and in written format, physical concepts of a certain complexity, making them understandable to non-specialist settings.
- Describe the laws that govern the quantum world: identify the postulates of quantum mechanics and develop an intuition of its characteristic properties.
- Describe certain paradigmatic quantum systems such as the Stern-Gerlach experience, the double slit or potential barriers (tunnelling effect).
- Describe unperturbed atomic structure and levels.
- Calculate the electronic structure of the hydrogen atom using formalism and the methods introduced in a general manner.
- Use approximate methods in simple models that describe the general characteristics and behaviour of highly complex physical systems.
- Use Hilbert's spaces and Hermitian and unitary operators.
- Use differential equations and orthogonal families of function.
- Work independently, take initiative itself, be able to organize to achieve results and to plan and execute a project.
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 |
|---|---|---|---|
| Exercise sessions (problem solving and seminars) | 22 | 0.88 | 1, 2, 7, 8, 9 |
| Study theory | 40 | 1.6 | 1, 3, 4, 5, 6, 8, 9 |
| Theory lectures | 28 | 1.12 | 1, 3, 4, 5, 6, 7, 8, 9 |
| Solve assigned problems | 51 | 2.04 | 1, 3, 4, 5, 7, 8, 9 |
Lectures
In the lecture sessions, we introduce the key concepts and methods that define the course contents. Before each face-to-face class, students are expected to familiarize themselves with the material made available in the form of notes, videos, or recommended readings.
Problem-Solving Sessions
The problem sets illustrate the application of the concepts learned to specific problems of pedagogical or practical relevance. They are also intended to help students strengthen their mathematical skills.
Some of the problems are solved in class by the instructor. Students are expected to have attempted these problems beforehand so that they can assess the accuracy of their solutions and incorporate any necessary corrections. Other problems are to be solved independently and submitted directly to the instructor.
A series of quizzes covering the different topics of the course will be available on the Moodle platform. These quizzes are designed to help students assess their level of understanding of the concepts throughout the semester. The quizzes are not graded; however, some of the topics covered may be included in the assessment tests.
Approximately four sessions of two hours each are scheduled during the semester in which students work on problems in randomly assigned groups of three to four members. These problems address selected topics in greater depth and provide opportunities to explore the application of concepts more thoroughly, as well as to learn new techniques.
Tutorials
Individual tutorials (and, when appropriate, group tutorials) will be used to address students’ questions and clarify doubts.
Non-Presential (Independent) Activities:
- Study and preparation of lecture material.
- Study and solution of the assigned problem sets prior to class.
- Completion of Moodle quizzes.
- Peer review and assessment of the special problem-solving sessions.
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| First evaluation | 40-45% redeemable | 3 | 0.12 | 1, 2, 3, 4, 8, 9 |
| Make up exam | 100% | 3 | 0.12 | 1, 3, 4, 5, 6, 7, 8, 9 |
| Assignment i and problem Sessions | 10-20% | 0 | 0 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 |
| Second evaluation | 42.5-45% redeemable | 3 | 0.12 | 1, 2, 3, 5, 6, 7, 8, 9 |
All evaluations will be written. Exams will be split into a Theory and Problems part of the same weight. Support texts may not be used during the exams, except for a mathematical formula sheet that will either be attached to the exam or prepared beforehand by the student. The first evaluation (with Theory and Problems) will be done after about 7 weeks and will include approximately half of the syllabus. The second will be done about 7 weeks later and will include the other half.
Both the first and the second partial exams will be redeemable (and with the possibility to improve the grade) at the end of the semester with a final evaluation or make up exam. In other words, there will be two partial exams and for those who want it or need it, there will be a make-up exam for the relevant parts. It is necessary to have a grade of at least 3 for each of the parts. In general, it is necessary to sit in both partials in order to be able to take the make-up exam. Special circumstances may be considered. The problem sessions will contribute up to two points to the mark of the partial examinations (not to the one of make-up exam). The student will be considered assessable if any of the partial or final examinations are handed in.
With respect to students approved for partials who present themselves to upload a grade (of the partials or overall), if the grade is higher than the previous one, the latter will be considered, and if it is lower, an average will be made at 75% previous grade 25% recovery grade. Students will a period of 15min period to decide if they go ahead with the final examination.
Single assessment
Students who have requested the single assessment modality will have to take a final test which will consist of: (i) a theory exam with theoretical questions of the whole course (ii) solve a series of exercises similar to those worked on in the Classroom Practice sessions, and (iii) once finished, will have to answer some oral questions about concepts developed in the seminar sessions. These tests will take place on the same day, time and place as the tests of the second part of the continuous assessment modality. The student's grade will be the weighted average of the three previous activities, where the theory exam will account for 40% of the grade, the problem exam 40% and the oral questions 20%. If the final grade does not reach 5, the student has another opportunity to pass the subject through the recovery exam that in general will coincide with the date of the retake exam, or on a date set by the degree coordinator. In this test 70% of the grade corresponding to the theory and the problems can be compensated. The oral part is not redeemable.
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 being graded with a 0. If the course syllabus stipulates that obtaining a minimum grade in that assessment activity is an essential requirement to pass the course, or if multiple irregularities occur in the assessment activities of 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 | first semester | morning-mixed |
| (PAUL) Classroom practices | 1 | Catalan | first semester | morning-mixed |
| (TE) Theory | 2 | Catalan | first semester | morning-mixed |
| (PAUL) Classroom practices | 2 | Catalan | first semester | morning-mixed |