F6082 Theoretical Physics 2

Faculty of Science
Spring 2017
Extent and Intensity
4/2. 5 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michael Krbek, Ph.D. (lecturer)
Mgr. Michael Krbek, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Mon 20. 2. to Mon 22. 5. Mon 13:00–14:50 F4,03017, Thu 14:00–15:50 F4,03017
  • Timetable of Seminar Groups:
F6082/01: Mon 20. 2. to Mon 22. 5. Fri 13:00–14:50 F4,03017
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The second part of the course is devoted to quantum mechanics and statistical physics.
Syllabus
  • A. Quantum physics
  • 1. Stern-Gerlach experiment and its modifications (Feynman) a. state vector, q-bit b. observables c. operators d. mean values and dispersion 2. Rotations in quantum mechanics, Stern-Gerlach continued a. Dirac's bra+ket formalism b. base change, linear combinations, superposition principle c. rotation operator, adjoints, inverse and unitary operators d. infinitesimal rotations, hermitean operators e. eigenvalues, eigenvectors, spectral decomposition f. measurement in quantum theory g. composition of rotations, quaternions h. other examples of two state systems, light polarisation, ammonia molecule, ... 3. Angular momentum and spin in quantum physics, time evolution a. infinitesimal rotations and angular momentum operators b. commutators, general uncertainty relations c. commuting operators, complete set of observables, degeneration d. complete set of observables for angular momentum, Jz, J^2, ladder operators e. unitarity of time evolution f. Hamiltonian as infinitesimal generator of time evolution g. operator exponential and the formal solution of time evolution of states. Schrödinger equation, stationary states d. spin ½ particle in magnetic field e. magnetic resonance 4. Coordinate representation, one continuous degree of freedom a. free particle on the circle b. harmonic oscillator algebraic method, coordinate representation of stationary states c. uncertainty relation for a,b. d. eigenstates for position and momentum, base change between continuous bases, Fourier series and transform e. potential barrier, the tunneling effect, scattering on a barrier 5. Two body problem in quantum physics a. translational and rotational symmetries, conservation laws b. momentum operator in coordinate representation c. orbital angular momentum in coordinate representation d. center of mass, relative position, analogy with classical mechanics e. complete set of observables H, Lz, L2, spherical functions f. vibration and rotation of diatomic molecules g. Coulomb interaction and the hydrogen atom 6. Approximate methods in quantum theory a. classical limit, correspondence principle b. stationary perturbation theory, anharmonic oscillator c. Ritz variational method d. quasi classical approximation 7. Systems of identical particles a. permutation operators, symmetry and antisymmetry b. bosons and fermions c. some results of indistinguishability of particles
  • B. Thermodynamics
  • 8. States, state variables, equations of state a. states, intensive and extensive quantities b. equilibrium and temperature, 0th law c. pressure, chemical potential, generalized work d. example equations of state: ideal gas, van der Waals gas, elastic rod, ... 9. 1st, 2nd and 3rd law of thermodynamics a. heat and capacities b. Carnot process c. equivalence of different formulations d. microscopic interpretation of entropy e. Gibbs-Duhem equation 10. Relations in thermodynamics a. thermodynamic potentials, energy, free energy, enthalpy, free enthalpy, Gibbs potential b. Legendre transform, Maxwell relations c. other relations d. some phase changes
  • C. Statistical physics
  • 11. Description of states in statistical physics, micro canonical distribution a. density operator formalism b. classical distribution function c. micro canonical ensemble d. contact with thermodynamics and information theory 12. Canonical and grand canonical distribution a. Bose-Einstein distribution b. Fermi-Dirac distribution c. Boltzmann distribution as a limit of BE a FD distributions d. classical statistical physics 13. Non stationary processes a. heat conduction, heat flow b. heat equation and its solutions
Literature
    recommended literature
  • WALECKA, John Dirk. Introduction to Modern Physics. Theoretical Foundations. World Scientific, 2008. ISBN 978-981-281-225-4. info
  • KREY, Uwe and Anthony OWEN. Basic Theoretical Physics. Berlin Heidelberg: Springer, 2007. ISBN 978-3-540-36804-5. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 1. vyd. Bratislava: Alfa, 1982, 357 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky 1. Mechanika. Elektrodynamika. první. Bratislava: Alfa, 1980. info
Teaching methods
Lectures and exercises.
Assessment methods
Two tests: 1st test: quantum physics, 2nd test: thermodynamics and statistical physics, each 1/6th of the final grade. Homework finished at least one week before oral examination, 1/3rd of the final grade. Oral examination, 1/3rd of the final grade
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2017, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2017/F6082