Elements of Quantum Mechanics 390-ERS-3EMK
Elements of Quantum Mechanics are the one semestral course of the subject. It includes 45 hours of the lecture and 45 hours of the discussion session (3 hours of the lecture and 3 hours of the discussion session per a week).
Educational profile: general academic.
Type of the studies: full-time.
Block (unit): theoretical physics, mandatory subject.
Field of knowledge and discipline of science: physical science, quantum mechanics.
Year of the studies, semester: 3rd year, 5th semester, undergraduate studies.
Introductory conditions: course of analysis, course of algebra, course of classical mechanics.
Didactic methods: lecture, solving the problems, homework, discussions, consultations, unassisted studying.
ECTS points: 9.
Balance sheet of the student's work: lecture (45 hours), discussion session (45 hours), homework (90 hours), discussions (5 hours), consultations (15 hours), unassisted studying (90 hours).
Quantitative indicators: lecture (2 ECTS points), discussion session (2 ECTS points), homework (2 ECTS points), discussions (0,5 ECTS points), consultations (0,5 ECTS points), unassisted studying (2 ECTS points).
The content of the course includes:
1) Physical basis of quantum mechanics - values of various physical constants describing phenomena on atomic scale. Fine structure constant.
Problems with describing a stable hydrogen atom and explaining its spectrum. Model of the atom according to Bohr - its advantages and disadvantages.
2) Postulates of quantum mechanics: observables, wave function, expected values of measurements, time evolution equation of wave function - Schroedinger equation, scattering states and bound states.
3) Simultaneously measurable operators, Heisenberg's principle of uncertainty.
4) Solving the Schroedinger equation in 1 dimension for specific energy potential functions: infinite square well, harmonic oscillator potential, finite square well. Energy levels of bound states, forms of wave functions.
5) Solving the Schroedinger equation in 1 dimension for a free particle, Gaussian wave function package, spreading of the wave package during time of evolution.
6) Scattering in 1 dimension for a finite square well and potential barrier, scattering matrix, probability of passage and reflection of the quantum particle. Tunnelling through the barrier in a classically forbidden area.
7) Schroedinger equation in 3 dimensions for spherically symmetrical potential, separation of equations, time independent Schroedinger equation. Wave function for angular equation - spherical harmonics. Solution of radial equation for Coulomb potential - energy levels, quantum numbers, wave function.
8) Angular momentum operators, algebra of operators, quantum numbers.
9) Spin operators, their algebra, matrix representations for spin 1/2 and spin 1.
Schroedinger equation for the spin 1/2 in a magnetic field. Stern-Gerlach experiment.
10) Identical particles in quantum mechanics, fermions and bosons. Two-particle states for fermions and bosons. The Pauli exclusion principle.
Periodic system of elements. Exchange forces.
Discussion session embraces the same scope of the program as the lecture does and comprises its illustration.
Type of course
Course coordinators
Learning outcomes
A student:
1. Knows role of quantitative models and abstract descriptions of physical object and physical phenomena in the area of fundamental parts of physics.
2. Knows restrictions of applicability for chosen physical theories, models of objects and description of physical phenomena.
3. Understands formal structure of basic physical theories, is able to apply appropriate mathematical tools for quantitative description of physical phenomena from chosen parts of physics.
4. Has knowledge of quantum mechanics foundations, of formalism and probabilistic interpretation of this theory, knows theoretical description and mathematical tools for analysis of chosen quantum systems.
5. Can understandingly and judgmentally examine professional literature and Internet sources, with regard to studied problems of quantum mechanics.
6. Understands structure of physics, treated as a branch of science, acquires cognisance of connections between its domains and theories, knows examples of false physical hypothesis and false physical theories.
7. Is capable to use known mathematical tools for defining and solving chosen problems of theoretical and experimental physics.
8. Can present theoretical formulation of quantum mechanics and is able to perform theoretical analysis of chosen quantum systems, using relevant mathematical tools.
9. Knows limitations of his knowledge and understands necessity of further education, of upgrading personal, professional and social competencies.
10. Is able to search individually informations in literature and Internet sources, including explorations in foreign languages.
Labels:
K_W22, K_U20.
Assessment criteria
Students take part in lectures broaden of computer simulations, illustrating transmitted contents. They are stimulated for asking the questions and for discussion.
Written and oral examinations undergo after the end of the course of Elements of Quantum Mechanics. They verify acquirement of knowledge.
Students get the series of questions, exercises and problems for individual and unassisted solving. Content of the series of questions is correlated with the lecture. During the course, students present solutions of given problems. Lecturer is advised to pay close attention to understanding used concepts and clarity of presentations. He stimulates students group for asking the questions and discussions. Lecturer tries to create sense of responsibility for team inside the students group and he encourages the group to join work.
Assessment of student learning is based on the grade, which includes:
1. Ability to solve the problems from define parts of quantum mechanics.
2. Ability to present the solutions.
3. Ability to discuss subjects and problems of the course.
4. Ability to use the literature and Internet sources.
5. Ability to collaborate inside the team.
6. Creative approach to solved problems.
Permanent grading by lecturer.
Final grade is expressed by the number established in the study regulation, which includes evaluation of the knowledge, abilities and competencies of the student.
Bibliography
1) Griffiths, Schroeter: Introduction to Quantum Mechanics"
2) L. I. Schiff: "Quantum mechanics"
3) L. D. Landau, E. M. Lifshitz: "Quantum Mechanics, Non-Relativistic Theory"
4) R. Liboff: "Introductory Quantum Mechanics"
5) I. Białynicki-Birula, M. Cieplak, J. Kamiński: "Theory of Quanta"
5) R. P. Feynman, R. B. Leighton, M. Sands: "Lectures on Physics", vol. 3: "Quantum Mechanics"
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: