Quantum Mechanics 390-FS2-1MKT
Quantum Mechanics is 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: 1st year, 1st semester, graduate studies.
Introductory conditions: course of analysis, course of algebra, course of classical mechanics, elements of classical electrodynamics, elements of
quantum mechnics
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 is following:
Finite-dimensional quantum mechanics.
Quantum models on the Hilbert space.
Bloch sphere.
Quantum states as vectors in Hilbert space.
Quantum states as operators.
Time evolution.
Observables and mixed states.
States of subsystems.
No-cloning and no-deleting theorems, quantum teleportation, superdense coding, quantum non-demolition measurements, quantum computers.
Interpretations of quantum mechanics.
Quantization, the quantum harmonic oscillator.
Uncertainty principles for canonical pairs of observables, entropic uncertainty principles, uncertainty for the energy observable.
Bell-type inequalities
Perturbation calculation for the time independent non-relativistic Schrödinger equation.
Calculation of the fine-structure of energetic levels for an electron in a hydrogen atom.
Calculus of variations applied to determine the energy levels of the ground state.
Pauli principle.
Time-depandent perturbation theory for the Schrödinger equation.
Transitions between levels for the 2-level system.
Pauli equation for a spin- ½ particle.
Minimal coupling rule in the electromagnetic field.
Stark effect in an electric field.
Klein-Gordon and Dirac equations for an electron.
Type of course
Requirements
Analysis I
Analysis II
Elements of Classical Electrodynamics
Elements of Quantum Mechanics
Prerequisites
Analysis I
Analysis II
Elements of Classical Electrodynamics
Elements of Quantum Mechanics
Prerequisites (description)
Course coordinators
Learning outcomes
A student:
1. She/he understands the role of physical theory and abstract description of physical objects and physical phenomena in the scope of selected issues of contemporary physics and its applications.
2. She/he has an extended knowledge of selected sections of theoretical physics, knows and understands basic theoretical concepts and mathematical models of selected systems and phenomena.
3. She/he is able to popularly quote contemporary achievements in the field of known branches of physics, present the latest practical solutions based on scientific research.
4. She/he knows how to apply theoretical physics methods to quantitative and qualitative analysis of selected systems and physical phenomena within the scope of the specialization program.
5. She/he is able to understand and critically use professional literature and Internet resources - including sources in English in relation to the studied physics problems.
Codes: K_W02, K_W09, K_U01, K_U09, K_U10.
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 Quantum Mechanics. They verify acquirement of knowledge.
Students get the series of questions, exercises and problems for individual and unassisted solving. 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) L. Schiff: "Quantum mechanics".
2) I. Białynicki-Birula, M. Cieplak, J. Kamiński: "Theory of Quanta".
3) L . D. Faddeev, O. A.Yakubovskiı̆: "Lectures on Quantum Mechanics for Mathematics Students".
4) M. Hirvensalo: "Quantum Computing".
5) S. A. Ponomarenko: "Quantum harmonic oscillator revisited: A Fourier transform approach", Am. J. Phys. 72, 1259 (2004).
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: