Quantum Mechanics

General characterization

Prerequisites

Previous approval in the following courses: Análise Matemática I, II e III and IV, Física I, II, III, A.L.G.A. and Vibrations and Waves.

Bibliography

• David J. Griffiths e Darrell F. Schroeter, Introduction to Quantum Mechanics 3rd Edition, Cambridge University Press, Cambridge, 2018
• F. Duarte Santos, A. Amorim, J. Batista, Mecânica Quântica, Fundação Calouste Gulbenkian, Lisboa, 2008.
• W. Greiner, Quantum mechanics: an introduction, Springer-Verlag, Berlin, 1994.
• S. Gasiorowicz, Quantum Physics, 2nd Ed., John Wiley and Sons, New York, 1996.
• C. Cohen Tannoudji, B. Diu et F. Laloë, Quantum mechanics, John Wiley & Sons, 1991.
• J. P. Santos e M. F. Laranjeira, Métodos Matemáticos para Físicos e Engenheiros, Fundação da Faculdade de Ciências e Tecnologia, Lisboa, 2004.

Teaching method

The course is organized in lectures where the theory is presented, and recitation sessions where problems are discussed with the instructor.

Evaluation method

**Article 1 – Knowledge Assessment Method**
1. In accordance with the FCT Assessment Regulations (Approved by the Executive Council on November 11, 2020), the assessment in "Quantum Mechanics" falls under Continuous Assessment.
2. The assessment consists of a single method for all students.
3. The grades mentioned in the following Articles are expressed on a scale from 0 to 20.

**Article 2 – Theoretical Classes**
1. The theoretical classes will start in the 1st week of classes (week of September 9th).

**Article 3 – Theoretical-Practical Classes**
1. The theoretical-practical classes (problems) will start in the 2nd week of classes (week of September 16th).
2. In the first theoretical-practical class of each shift, the attendance of students in the respective shifts will be confirmed.
3. Students who do not comply with point 2 will have their enrollment in the theoretical-practical shift canceled in the CLIP.
4. Within the limits of available slots, shift changes may be accepted during the first week of theoretical-practical classes. For this, students must contact the theoretical-practical class teacher by email.
5. Active participation in at least 2/3 of the theoretical-practical classes from the 1st class (week of September 16th) is mandatory (9 classes).
6. Justifications for absences from theoretical-practical classes will not be accepted. Students must manage the possibility of missing 1/3 of the classes to use these absences for potential commitments or unforeseen situations, including occasional illnesses.

**Article 4 – Attendance**
1. Students who comply with point 5 of Art. 3 and achieve a theoretical-practical grade (NTP) of 10 or higher, obtain attendance in the course with a grade equal to NTP.
2. The attendance obtained in the academic years 2022/23 and 2023/24 is valid for the current academic year. Consequently, they should not enroll in theoretical-practical shifts and are admitted to all tests and exams. Attendance obtained in academic years prior to 2022/23 is valid for the current academic year, however its grade is not used in the calculation of the final grade.
3. The list of students who obtained attendance in the academic years mentioned in point 2 of this Article is available in CLIP under "Support Documentation > Others > MQ_2425_Frequency_Previous_Years.pdf".
4. If a student who obtained attendance in previous academic years is not listed, they must send an email to the course coordinator by 5 PM on September 20th (Friday), with the subject “MQ – Previous Attendance”, their full name, current student number (and previous number if applicable), the year they obtained the attendance, and a copy of the record (available in CLIP) showing that they obtained attendance.
5. From the date mentioned in point 4, all students not listed in point 3 will be considered as not having attendance.

**Article 5 – Assessment**
1. The theoretical component grade (NT) is the arithmetic average, rounded to the nearest whole number, of the grades obtained in the 2 tests (each test grade is rounded to one decimal place), or the final exam grade, rounded to the nearest whole number.
2. Students who achieve a theoretical grade (NT) of 10 or higher pass the theoretical component.
3. Students who obtain a final continuous assessment grade (NF) of 7, 8, or 9 are admitted to an extra exam at the end of the semester, which may allow them to achieve a maximum of 10 in NF.
4. The theoretical-practical component grade (NTP) is the arithmetic average, rounded to the nearest whole number, of the two highest grades obtained in the mini-tests (Nm) given in the theoretical-practical classes and the 3 group practical assignments (NTG) completed outside class hours.
5. Absences from mini-tests will result in a grade of zero. If a student misses at least two assessment moments, a small oral assessment will be conducted, which will count as a mini-test.
6. The 3 practical assignments are mandatory.
7. NTP is calculated as follows: NTP = 0.5 Nm + 0.5 NTG.
8. Active participation in classes may be compensated by adding one point to NTP, not exceeding 20 points.

**Article 6 – Tests and Exams**
1. Registration for tests in CLIP is mandatory.
2. Only students who have obtained attendance or already had attendance are admitted to the 2nd test.
3. Each test will primarily cover all the material taught in the theoretical classes up to the class before the test.
4. Although test assessment is not cumulative, due to the nature of the topics covered in this course, an assessment element may include knowledge from previous assessments.
5. Tests are conducted in person, preferably during the theoretical class hours.
6. During the assessment, students are only allowed to have:
   a. Pen/ballpoint pen;
   b. Photo ID.
7. The use of electronic devices, such as calculators and mobile phones (which must be turned off), is not permitted during the tests.
8. It is not permitted to remove the pages from the test booklets containing the questions and the students'' answers.
9. The test will be annulled if points 6, 7, or 8 are not complied with.
10. Students who commit fraud in an assessment (Test or Exam) will have the test annulled, will automatically fail the course in the current academic year, and will lose attendance if they obtained it in previous academic years, which means they must obtain attendance in the next academic year. In cases of serious misconduct, disciplinary action may be taken against the student(s) who committed the fraud.

**Article 7 – Final Grade**
1. The final grade (NF) for students who have obtained attendance in the current or the two previous academic years is calculated as follows, rounded to the nearest whole number:
   a. NT is worth 70%;
   b. NTP is worth 30%.
2. The final grade for students who obtained attendance in an academic year prior to 2022/2023 is equal to the NT grade, rounded to the nearest whole number.
3. Students who simultaneously comply with point 1 of Art. 4, point 2 of Art. 5, and obtain a final grade of 10 or higher pass the course.
4. Students who comply with point 3 and obtain a final grade of 17 or higher are admitted to an oral exam.
5. In the oral exam mentioned in the previous point, students can increase or decrease their final grade, with a minimum guaranteed grade of 17.
6. Absence from the oral exam mentioned in the previous point implies acceptance of a final grade of 17.
7. In other cases not covered by the previous points and Articles, the student fails the course.

**Article 8 – Grade Improvement**
1. Students wishing to improve their grade must comply with the legal formalities for registration.
2. Students who passed the course in the current academic year of 2024/2025, or in the academic year 2023/24, can improve their final grade.
3. If the exam grade is higher than the grade to be improved, the final grade is the exam improvement grade, rounded to the nearest whole number.
4. Students who obtain a final grade described in point 3 of 17 or higher are admitted to an oral exam.
5. In the oral exam mentioned in the previous point, students can increase or decrease their final grade, with a minimum guaranteed grade of 17.
6. Absence from the oral exam mentioned in the previous point implies acceptance of a final grade of 17.
7. In other cases not covered by the previous points, the student does not improve their grade.

**Article 9 – Working Students**
1. Students are considered as having Working Student (TE) status if they are listed as such in the CLIP records.
2. Students should inform the course coordinator of their status as soon as possible.
3. Students who comply with point 2 of Art. 5 pass the course.
4. Working students, like other students, must take the assessments according to the previously published schedule.

**Article 10 – Classroom Conduct**
1. To ensure everyone benefits from the learning experience, students are expected to adhere to the following conduct rules during class:
   a. Punctuality: Students should be in the classroom at the start time. Teachers will mark students arriving more than 5 minutes late as absent;
   b. Class preparation and participation: Active participation requires students to prepare the material presented and discussed in class and contribute to discussions.

**Article 11 – Others**
1. When contacting teachers via email, students must indicate in the "Subject" the following information: "MQ - Shift – Name – Student Number – Subject".
2. Emails with questions that are answered in the previous Articles or on the course''s CLIP page will not be answered.

Subject matter

1. Historical introduction
2. From classical to quantum
3. The mathematics of Quantum Mechanics
4. The postulates of Quantum Mechanics
5. Study of unidimensional simple systems
6. Particle scattering and barrier penetration
7. Systems of particles
8. The Schrödinger equation in three dimensions
9. Angular momentum
10. Quantum states in three dimensions
11. Methods of approximation - perturbation theory
12. Quantum computing

Programs

Programs where the course is taught: