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Additional chapters for quantum mechanics

ВК6

Вибіркова дисципліна для ОП

First

2023/2024

7 Semester

4

The learning outcomes are knowledge of the fundamental laws of quantum mechanics, the theory of quantum transitions, representation of the amplitude of the transition through the integral along trajectories, application of this representation to obtain approximations in interaction with the external field and systems of interacting particles. Also, as a result, students are introduced to the basic approximations of the equations of quantum mechanics and the basic models of behavior of particles in the external field, as well as able to solve complex specialized problems and practical problems in physics in professional activities or in further learning and methods of physics and is characterized by complexity and uncertainty of conditions.

Full-time form

Know the basic laws of quantum mechanics, mathematical analysis, ordinary differential equations, mathematical physics. In particular, to know the Euler-Lagrange equation, Green's function for differential equations, Ostrogradsky-Gauss and Stokes theorems, Legendre polynomials, spherical functions, cylindrical functions, Bessel, Hankel, Neumann and MacDonald functions. Remember the expressions for the gradient, divergence, rotor and Laplace operator in cylindrical and spherical coordinate systems. Be able to apply previous knowledge from the courses of mathematical analysis, mathematical physics, basics of vector and tensor analysis and differential equations to solve algebraic and differential equations and systems. Have basic skills in calculating derivatives, integrals, operations on operations with vectors, graphically plotting functions, defining and decomposing functions into series and Fourier integrals.

The discipline "Additional chapters of quantum mechanics" is a component of professional training of specialists of educational and qualification level "Bachelor of Physics" and basic for the study of theoretical physics. The aim of the course is to master the knowledge of special methods of theoretical physics, which are necessary for students to creatively solve complex physical problems using modern methods and approaches.

1. A.M. Ermolaev, G.I. Rashba, LECTURES ON QUANTUM STATISTICS AND KINETICS, Basic concepts of quantum mechanics, Study Guide, Kharkov 2007. 2. M. Chaichian, A. Demichev, Path integral in Physics, Vol. 1, IoP, 2001 3. H. Kleinert, Path integral in Quantum Mechanics, Statistics, Polimer Physics, Vol. 1 and 2, 2002. 4. Wipf, Path Integrals. 2002 5. R. Feynman, A. Hibbs, Quantum mechanics and integrals on trajectories. - M. Fizmatlit. 1995 6. Zinn-Justin, Continuous integral in quantum mechanics. - M. Fizmatlit. 2006

The total amount of 120 hours, including: Lectures - 14 hours. Practical classes - 30 hours. Consultations - 1 hour. Independent work - 75 hours.

Forms of current control: assessment of homework, written independent assignments, tests and tests performed by students during practical classes. The student can receive a maximum of 40 points for homework, independent assignments, oral answers, tests, additions to practical classes. A student is not admitted to the test if he / she scored less than 24 points during the semester. Final assessment is in the form of a test. You can get a maximum of 60 points on the test.

Ukrainian