Infopaket

Quantum mechanics

ОК 26

Обов’язкова дисципліна для ОП

First

2022/2023

5 Semester

6

The student must know: General physical and mathematical methods for describing the phenomena of the microworld using the wave function based on the basic stationary and nonstationary Schrödinger equations. The theory of operators and methods of their use in quantum mechanics. General approaches to the calculation of mechanical, electronic, optical, magnetic and other characteristics of physical microsystems. Basic methods of calculations using the quasiclassical method, direct variational method and methods of stationary and nonstationary perturbation theory. Features of interaction of quantum systems with electromagnetic fields. The theory of spontaneous and indused radiation in model and real systems. Density matrix methods for analyzing the evolution of quantum systems under stochastic relaxation. Principles of construction and methods of using relativistic Klein-Gordon-Fock and Dirac equations of quantum mechanics.

Full-time form

To sufficiently master the discipline "Quantum Mechanics" requires knowledge of mathematical courses: "Mathematical Analysis", "Linear Algebra", "Differential Equations", " Methods of Mathematical Physics" and courses in general physics "Atomic Physics", "Optics" and theoretical physics ", in particular, "Theoretical Mechanics", "Electrodynamics".

1.History and preconditions of Quantum Mechanics (QM). Statistical nature of microworld phenomena. Interpretation of wave function. Postulates of QM. Equations for eigenvalues ​​and eigenfunctions. Heisenberg-Robertson and Heisenberg uncertainty relations. Stationary and nonstationary Schrödinger equations. Continuity equation. The motion of a particle in a field of central force. Hydrogen-like atoms, simple molecules and magnetic properties of atoms. Representation theory for stationary and nonstationary systems. Spin and spin-dependent processes in QM. Pauli equation. Zeeman effects. Pauli principle. 2.Approximate methods in QM. Interaction of electromagnetic field with quantum systems. Selection rules. Theory of spontaneous and indiced radiation. Pure and mixed states. Density matrix method. 3.Relativistic equations of QM.Continuity equation and current density vector for Dirac particles. Nonrelativistic approximation of Dirac's equation. Quantum theory of spin operator.

1. Висоцький В.І. Квантова механіка та її використання в прикладній фізиці: Підручник.-Київ, Видавництво КНУШ, 2008. 2. D.I.Blokhintsev. Quantum mechanics, Springer Science & Business Media, 2012. 3. Вакарчук І.О. Квантова механіка: Підручник.- Львів, Видавництво Львівського університету, 1998. 4. L D Landau, E. M. Lifshitz. Quantum Mechanics: Non-Relativistic Theory, Elsevier, 2013. 5. Находкін М.Г., Шека Д.І. Атомна фізика: Підручник.- К., 2002. 6. Висоцький В.І. Максюта М.В., Ястремський І.О. Збірник задач з квантвої механіки, .- Київ, Видавництво КНУШ, 2020.

Lectures, practical classes, individual independent work.

Solving problems in practical classes for the semester - a maximum of 10 points; Testing (2 tests of 10 points); Homework and individual tasks - 10 points; Modular test (2 Modular tests of 10 points each); Exam - 40 points. The exam ticket consists of 2 theoretical questions (answers, questions are evaluated on 10 points) and 2 tasks, which are evaluated on 10 points. In total, you can get from 0 to 40 points for the exam. The condition for achieving a positive grade for the discipline is to obtain at least 60 points, the grade for the exam can not be less than 24 points. Conditions for admission to the final exam: a bachelor's degree in total is not less than the critical-calculated minimum for the semester. Bachelors who scored less than the critical minimum of 36 during the semester must write an additional test in order to be admitted to the exam.

Ukrainian