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Quantum Mechanics

Code: 100171
Credits: 6
2026/2027
Degree programme Type Course
Physics OP 4

Contact lecturer

Name :
Rafel Escribano Carrascosa
Email :
rafel.escribano@uab.cat

Teaching staff

Noé Duarte González

Group languages

You can consult this information at the end of the document.

Prerequisites

Prior knowledge of quantum physics, Hilbert spaces, operators, and group theory is required, so it is advisable to have studied Quantum Physics I, Quantum Physics II and Advanced Mathematical Methods.

Objectives

The objective of this subject is for students to master various methods and formal aspects of Quantum Mechanics that allow them to deepen their knowledge and that have a wide range of applications in various areas of modern physics such as atomic, nuclear, particle, condensed matter, solid state, photonics, etc. The use of Hilbert spaces will be explored in depth, the different time evolution images will be introduced as well as the unitary operators of time evolution and those of symmetries realizations, continuous and discrete. The most important applications to assimilate are the continuous spectrum operators, the quantum-mechanical addition of angular momenta, identical particles and the theory of time-dependent perturbations, as well as the notable examples of time-dependent potentials.

Learning outcomes

  1. Communicate complex information in an effective, clear and concise manner, either orally, in writing or through ICTs, in front of both specialist and general publics.
  2. Use critical reasoning, show analytical skills, correctly use technical language and develop logical arguments
  3. Work independently, take initiative itself, be able to organize to achieve results and to plan and execute a project.
  4. Working in groups, assume shared responsibilities and interact professionally and constructively with others, showing absolute respect for their rights.
  5. List and describe the principles of quantum mechanics.
  6. Describe the differences between pure and mixed states and their formalism.
  7. Describe the dynamics of a system and its evolution on the basis of the time evolution operator and distinct image equivalents.
  8. Describe Ehrenfest's theorem.
  9. Describe the generator concept for a continuous transformation and the associated symmetry.
  10. Describe the composition of angular momenta.
  11. Describe discrete transformations in addition to the concept of identical particles and particle exchange, and their consequences.
  12. Describe interaction in quantum mechanics, the image of interaction and the development of perturbation theory.
  13. Calculate the probability of measuring an observable within a quantum system.
  14. Correctly consider the evolution of a quantum system.
  15. Correctly use translation and rotation operators on a given quantum system.
  16. Correctly carry out the composition of angular momenta.
  17. Calculate Clebsch-Gordan coefficients and be able to use the tables.
  18. Correctly predict the result of applying discrete transformations as parity or temporary investment on a system.
  19. Calculate the evolution of a system to which we apply a time-dependent potential.
  20. Analyse new and old quantum experiments from different points of view to consolidate the foundations of quantum formalism and to consider unconventional views.
  21. Analyse the implications of new approaches with specific proposals and test their validity in the context of quantum mechanics.
  22. Relate recent research results to certain fundamental aspects of quantum mechanics.
  23. Relate some of the applications of quantum mechanics with current technological developments.
  24. Identify the essential features of the quantum problem by translating these into operator terms and quantum states to describe the system and relevant observables.
  25. Apply different equivalent ways of solving the same problem, using for example, distinct images or equivalent descriptions related to unitary operators.
  26. Distinguish between the assumptions implicit in a given problem and the consequences of eliminating these and, therefore, learning to generalize solutions.
  27. Rigorously manipulate the properties of Hilbert's spaces and of the direct product and sum of spaces.
  28. Correctly use continuous bases and Dirac's notation.
  29. Use the spectral and matrix representation of Hermitian and unitary operators.
  30. Develop the capacity to relate the mathematical formalism of quantum mechanics experiments with the physical world.

Contents

1) Theory of Angular Momentum: Addition of Angular Momenta

2) Symmetry in Quantum Mechanics: Symmetries and Conservation Laws; Discrete Symmetries (Parity, Time Reversal)

3) Approximation Methods: Time-Dependent Potentials; Time-Dependent Perturbation Theory

4) Scattering Theory: The Scattering Amplitude; The Born Approximation; Phase Shifts and Partial Waves

5) Identical Particles: Quantum Fields; Second Quantization

6) Relativistic Quantum Mechanics: The Klein-Gordon Equation; The Dirac Equation

Learning activities and methodology

Title Hours ECTS Learning outcomes
Exercises 16 0.64 1, 2, 3, 4, 7, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30
Discussion, Work Groups, Group Exercises 24 0.96 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30
Theory Lessons 33 1.32 1, 2, 3, 7, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30
Study of Theoretical Foundations 48 1.92 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30

Theory Lessons and Exercises.

Classwork and Homework.

In this course, the use of Artificial Intelligence (AI) technologies is prohibited at all stages of the learning and assessment process. Any work containing AI-generated content will be considered a violation of academic integrity and may result in a partial or complete reduction of the activity grade, or more severe disciplinary sanctions in cases of serious misconduct.

Annotation: within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

Assessment

Continuous assessment activities

Title Weight Hours ECTS Learning outcomes
Resolution and presentation of assignments: second part topics 10% 10 0.4 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30
Make-up Exam: all topics 80% 3 0.12 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30
Exam: first part topics 40% 3 0.12 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30
Resolution and presentation of assignments: first part topics 10% 10 0.4 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30
Exam: second part topics 40% 3 0.12 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30

Exam for the topics in the first partial;

Resolution and presentation of assignments for the topics in the first partial;

Exam for the topics in the second partial;

Resolution and presentation of assignments for the topics in the second partial;

Make-up exam: all topics;

To participate in the make-up exam, you must have been assessed in both partial exams without requiring a minimum grade;

The make-up exam covers the entire subject;

You may attend the make-up exam to improve your grade. If so, your final grade for the exam portion will be the one obtained in the make-up exam.

Single assessment: The students that opted for single assessment evaluation will have to perform a final evaluation that will first consist of a test of the whole syllabus. This test will take place on the same date, time, and place as the test of the continuous assessment modality. Besides, before the exam, the student will deliver 2 deliveries consisting in resolved exercises of a selected set of exercises proposed at an earlier date. For the mark, 80% of the final mark will come from the exam and each of the deliveries will count 10%. The students that opted for single assessment evaluation will have the chance of passing the module or improving their mark at the same re-evaluation test as the students that had opted for the continuous assessment option (both exams will be identical and will take place on the same day, time, and in the same place). However, it is mandatory to at least have taken the previous final test. At this test, it is only possible to improve the mark of the exam. The part of the deliveries can not be improved in the re-evaluation.

Bibliography

  • "Modern Quantum Mechanics", J. J. Sakurai and J. Napolitano, Cambridge University Press, 2021
  • "Quantum Mechanics", D. Tong, Cambridge University Press, 2025
  • "Introduction to Quantum Mechanics", D. J. Griffiths and D. F. Schroeter, Cambridge University Press, 2018

Software

Software is not required.

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 English first semester morning-mixed
(PAUL) Classroom practices 1 English first semester morning-mixed