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Course, academic year 2022/2023
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Introductory Seminar on Theoretical Physics - NOFY070
Title: Proseminář z teoretické fyziky
Guaranteed by: Laboratory of General Physics Education (32-KVOF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: summer
E-Credits: 2
Hours per week, examination: summer s.:0/2, C [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Additional information: http://utf.mff.cuni.cz/vyuka/NOFY070
Guarantor: prof. RNDr. Pavel Krtouš, Ph.D.
RNDr. Otakar Svítek, Ph.D.
Classification: Physics > Theoretical and Math. Physics
Annotation -
Last update: doc. RNDr. Karel Houfek, Ph.D. (14.05.2021)
Vector and tensor calculus, curvilinear coordinates. Introduction to distributions, Fourier transformation, Green functions. Introduction to classical field theory. Multipole expansion in a tensor form. Feynman formulation of quantum mechanics.
Course completion requirements - Czech
Last update: prof. RNDr. Pavel Krtouš, Ph.D. (29.01.2021)

Zápočet bude udělen za dostatečnou účast na hodinách a správné vypracování domácích úloh.

Povaha kontroly splnění podmínek pro udělení zápočtu vylučuje opakování této kontroly, tedy zápočet se opakovat nedá.

Literature - Czech
Last update: prof. RNDr. Pavel Krtouš, Ph.D. (29.01.2021)

K. Kuchař: Základy obecné teorie relativity, Academia, Praha 1968.

L. Schwartz: Matematické metody ve fyzice, SNTL, Praha 1972

J. W. Leech: Klasická mechanika, SNTL, Praha 1970.

R. P. Feynman, R. B. Leighton, M. L. Sands, Feynmanovy přednášky z fyziky 3, Fragment, Havlíčkův Brod 2002.

R. P. Feynman: Neobyčejná teorie světla a látky, Aurora, Praha 2001.

Syllabus -
Last update: prof. RNDr. Pavel Krtouš, Ph.D. (29.01.2021)
Vectors and tensors.
Affine space, vectors and linear forms, tensors, coordinate transformations, diagrammatic notation, scalar product and metric.
Curvilinear coordinates and vector analysis.
Tensor fields, gradient and nabla-operator, curvilinear coordinates, triads. Integrating vectors and tensors.
Introduction to distributions.
Basic definitions and properties, δ-distribution, derivatives of non-smooth functions, regularization of 1/x. Fourier transformation of distribution, examples. Distribution on manifolds, characteristic function, surface and linear δ-distributions and their derivatives. Aplications: point, linear and surface sources, dipoles, boundary conditions for electrostatic a magnetostatic, electric field near conductors.
Green functions
Green functions in one variable. Green function for Laplace operator, Laplace equation on a domain with a boundary, heat equation, perturbative solution of Schrödinger equation with potential.
Classical field theory
Lagrange and Hamilton formalism for fields, scalar and electromagnetic field, gauge symmetry.
Supplements for classical electrodynamics
Multipole expansion in terms of tensors. Description of continuum is spacetime, stress-energy tensor, electric current density, conservation laws.
From sum over trajectories to solution of differential equations.
Feynman's formulation of quantum mechanics: quantum histories, quantum indistinguishability, amplitude rules, measurement model. Path integral, amplitude of free particle evolution, perturbative solution of Schrödinger equation.
 
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