ECTS - Quantum Mechanics
Quantum Mechanics (PHYS501) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Quantum Mechanics | PHYS501 | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| For any student, at least a quantum physics or an introductory quantum mechanics course must have been taken previously. For undergraduate students who are to take this course as an elective course MATH 275 and MATH 276 or their equivalents are additional pre-requisites. |
| Course Language | English |
|---|---|
| Course Type | N/A |
| Course Level | Natural & Applied Sciences Master's Degree |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Discussion, Question and Answer, Drill and Practice, Problem Solving. |
| Course Lecturer(s) |
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| Course Objectives | [1] To introduce the student with the experimental concepts of quantum mechanics (via the Stern-Gerlach experiment). [2] To give the student a comprehensive and rigorous mathematical foundation on which quantum mechanics will be erected. [3] To offer a solid understanding of angular momentum theory in quantum mechanics. [4] (If time permits, i.e., optionally) to convey to the student the importance of symmetry in quantum mechanics. [5] To provide the student with a solid understanding of approximation methods and with a power to apply these to the practical problems. |
| Course Learning Outcomes |
The students who succeeded in this course;
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| Course Content | Fundamental concepts of quantum mechanics, quantum dynamics, theory of angular momentum, symmetry in quantum mechanics, approximation methods. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | FUNDAMENTAL CONCEPTS: the Stern-Gerlach experiment; kets, bras, and operators; base kets and matrix representations; measurements, observables, and the uncertainty relations. | Sakurai 1-23 |
| 2 | FUNDAMENTAL CONCEPTS (cont’d): change of basis; position, momentum, and translation. | Sakurai 23-51 |
| 3 | FUNDAMENTAL CONCEPTS (cont’d): wave functions in position and momentum space. QUANTUM DYNAMICS: time evolution and the Schrödinger equation. | Sakurai 51-60 and 68-80 |
| 4 | QUANTUM DYNAMICS (cont’d): the Schrödinger versus the Heisenberg picture; simple harmonic oscillator. | Sakurai 80-97 |
| 5 | QUANTUM DYNAMICS (cont’d): Schrödinger’s wave equation; propagators and Feynman path integrals. | Sakurai 97-123 |
| 6 | QUANTUM DYNAMICS (cont’d): potentials and gauge transformations. THEORY OF ANGULAR MOMENTUM: rotations and angular momentum commutation relations. | Sakurai 123-143 and 152-158 |
| 7 | Midterm Examination | |
| 8 | THEORY OF ANGULAR MOMENTUM (cont’d): spin ½ systems and finite rotations; SO(3) and SU(2), Euler rotations. | Sakurai 158-174 |
| 9 | THEORY OF ANGULAR MOMENTUM (cont’d): density operators and pure and versus mixed ensembles; eigenvalues and eigenstates of angular momentum; orbital angular momentum. | Sakurai 174-203 |
| 10 | THEORY OF ANGULAR MOMENTUM (cont’d): addition of angular momentum; Schwinger’s oscillator model of angular momentum. | Sakurai 203-223 |
| 11 | THEORY OF ANGULAR MOMENTUM (cont’d): spin correlation measurements and Bell’s inequality; tensor operators. | Sakurai 223-242 |
| 12 | SYMMETRY in QUANTUM MECHANICS: symmetries, conservation laws, and degeneracies; discrete symmetries, parity, or space inversion; lattice translation as a discrete symmetry. | Sakurai 248-266 |
| 13 | SYMMETRY in QUANTUM MECHANICS (cont’d): the time-reversal discrete symmetry. APPROXIMATION METHODS: time-independent perturbation theory for nondegenerate cases. | Sakurai 266-282 and 285-298 |
| 14 | APPROXIMATION METHODS (cont’d): time-independent perturbation theory for degenerate cases; hydrogen-like atoms, fine structure and the Zeeman effect; variational methods. | Sakurai 298-316 |
| 15 | APPROXIMATION METHODS (cont’d): time-dependent potentials, the interaction picture; time-dependent perturbation theory; applications to interactions with the classical radiation field; energy shift and decay width. | Sakurai 316-345 |
| 16 | Final Exam |
Sources
| Course Book | 1. Modern Quantum Mechanics, J. J. Sakurai, Revised Edition, Addison-Wesley. |
|---|---|
| Other Sources | 2. Quantum Mechanics, E. Merzbacher, 3rd Edition, Wiley. |
| 3. Lectures of Quantum Mechanics, G. Baym, Benjamin-Cummings. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | 1 | 5 |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 12 | 30 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 1 | 30 |
| Final Exam/Final Jury | 1 | 35 |
| Toplam | 15 | 100 |
| Percentage of Semester Work | 65 |
|---|---|
| Percentage of Final Work | 35 |
| Total | 100 |
Course Category
| Core Courses | |
|---|---|
| Major Area Courses | X |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Acquiring core knowledge of theoretical and mathematical physics together with their research methodologies. | X | ||||
| 2 | Gaining a solid understanding of the physical universe together with the laws governing it. | X | ||||
| 3 | Developing a working research skill and strategies of problem solving skills in theoretical, experimental, and/or simulation physics. | X | ||||
| 4 | Developing and maintaining a positive attitude toward critical questioning, creative thinking, and formulating new ideas both conceptually and mathematically. | X | ||||
| 5 | Ability to sense, identify, and handle the problems in theoretical, experimental, or applied physics, or in real-life industrial problems. | X | ||||
| 6 | Ability to apply the accumulated knowledge in constructing mathematical models, determining a strategy for its solution, making necessary and appropriate approximations, evaluating and assessing the correctness and reliability of the procured solution. | X | ||||
| 7 | Ability to communicate and discuss physical concepts, processes, and the newly obtained results with the colleagues all around the world both verbally and in written form as proceedings and research papers. | X | ||||
| 8 | Reaching and excelling an advanced level of knowledge and skills in one or more of the disciplines offered. | X | ||||
| 9 | An ability to produce, report and present an original or known scientific body of knowledge. | X | ||||
| 10 | An ability to make methodological scientific research. | X | ||||
| 11 | An ability to use existing physics knowledge to analyze, to determine a methodology of solution (theoretical/mathematical/experimental) and to solve a problem. | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | 16 | 3 | 48 |
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 2 | 28 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 12 | 2 | 24 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 1 | 10 | 10 |
| Prepration of Final Exams/Final Jury | 1 | 15 | 15 |
| Total Workload | 125 | ||