Quantum Mechanics 2
0800-MEKW2
1. Symmetries in quantum mechanics
2. Lorentz transformation applied to equations of the relativistic quantum mechanics equations.
3. Klein-Gordon and Dirac equations (postulates leading to these equations and solutions obtained in the spherically symmetrical case of the hydrogen atom; Zitterbewegung; Klein paradox).
4. Introduction of even and odd operators.
5. Non-relativistic boundary of the Dirac equation; Levy-Leblond equation (kinetic and atomic balance).
6. Variational approach to determining eigen-states of the Dirac equation.
7. Lorentz transformation and Dirac equation; transformational properties of the wave function.
Total student workload
participation in the lectures - 30 hours
participation in the discussions - 30 hours
Time dedicated to the individual work with the student (80h.):
- preparation of the lecture - 20 hours
- preparation of the discussions - 10 hours
- reading of the literature materials used in the lecture - 20 hours
- preparation for the exams - 20 hours
- preparation for the tests - 10 hours
Total of 140 hours ( 5 ECTS)
Learning outcomes - knowledge
K_W01 - the student has extended knowledge of quantum physics: Lorentz invariance of relativistic equations;
K_W02 - the student has in-depth knowledge of advanced relativistic quantum mechanics;
K_W03 - the student knows the basic concepts and definitions needed for the theoretical description the of relativistic quantum mechanics and understands the importance of symmetry in the description of quantum systems;
K_W04 - the student has knowledge of the description of the relativistic quantum particles in relation to the appearance of antiparticles and virtual particles;
K_W05 - the student has knowledge of the current development in the area of the relativistic quantum mechanics
The above-mentioned topics implement the following directional effects:
K_W01, K_W03, K_W04, and K_W05 for physics s2.
Learning outcomes - skills
K_U01 - the student is able to solve the equations of relativistic quantum mechanics and to point out problems related to the no existence of a single particle in the relativistic quantum mechanics;
K_U02 - the student is prepared for further, more advanced studies of the relativistic quantum mechanics;
K_U04 - the student is able to find necessary information in specialist literature concerning the above topics.
The above-mentioned subjects implement the following directional effects:
K_U03 and K_U04 for physics s2.
Learning outcomes - social competencies
K_K01 - the student appreciates the role of natural sciences and understands the need for further scientific research.
Effects K_K01 and K_K03 for physics s2
Teaching methods
Lecture & exercises
Expository teaching methods
- informative (conventional) lecture
Exploratory teaching methods
- classic problem-solving
- practical
Type of course
compulsory course
Prerequisites
For the knowledge absobsion of the lecture as well its application in practical exercises student should have skils and knowledge on the level of the first course of Quantum Mechanics and Mathematical Analysis.
Course coordinators
Assessment criteria
The course consists of 30 h. of lecture and 30h. of exercises. The exercises are credited on the base of activity and two tests.
The lecture is credited on the base of positive exercises credit
and the exam from theoretical as well practical knowledge.
The written egzam ratings and evaluation:
50-60% points - 3
60-70% points - 3+
70-80% points - 4
80-90% points - 4+
90-100% points - 5
The same criteria of evaluation apply to the exercises.
Bibliography
1. S. J. Gustafson, I. M. Sigal, Mathematical Concepts of Quantum
Mechanics, Springer, Berlin 2003.
2. M. Grabowski, R. S. Ingarden, Mechanika Kwantowa - ujęcie w
przestrzeni Hilberta, PWN, Warszawa 1989.
3. J. J. Sakurai, Advanced Quantum Mechanics, Addison-Wesley, New York 1987.
4. W. Greiner, Relativistic Quantum Mechanics - Wave Equations,
Springer, Berlin 2000.
5. A. S. Davydov, Mechanika Kwantowa, PWN, Warszawa 1978.
6. L. Schiff, Mechanika Kwantowa, PWN, Warszawa 1977.
Additional information
Additional information (registration calendar, class conductors,
localization and schedules of classes), might be available in the USOSweb system: