UFDF007 Quantum Mechanics II

Faculty of Philosophy and Science in Opava
Winter 2013
Extent and Intensity
0/0. 0 credit(s). Type of Completion: dzk.
Guaranteed by
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a continuation of the course of Quantum Mechanics I. The new course is extended and supplemented. In the beginning approximate methods of quantum mechanics are shown, namely, generalized perturbation theory and variational methods. In the following, the theory of multi-particle systems, quantum scattering theory, interaction of radiation with matter, and relativistic quantum mechanics are discussed. The course is closed by part which sum up a significance of symmetries and conservation laws in quantum mechanics.
Syllabus
  • Mathematical basis of Quantum Mechanics: Axioms of Quantum Mechanics
    theory of representations (coordinate, momentum, energy), unitary
    transformations, pictures of Quantum Mechanics (Schrödinger, Heisenberg,
    Dirac) pure and mixed states, density operator.
    Approximated methods of quantum theory: Generalized perturbation theory
    variational method.
    Angular momentum II: Operator of generalized angular momentum addition of
    angular momenta, Clebsch-Gordon coefficients spin-orbit and spin-spin
    interactions fine structure of hydrogen.
    Multi-particle systems: Wavefunction and its physical meaning spin variables
    systems of identical particles exchange operator symmetric and
    antisymmetric wavefunctions, Pauli exclusion principle bosons and fermions.
    Helium: Calculation of energy levels by perturbative and variational methods
    two-electron spin functions excited states orthohelium and parahelium.
    Elementary theory of molecules: Adiabatic approximation hydrogen molecule
    vibrational, rotational and electron states of two-atom molecules.
    Quantum scattering theory: Partial wave analysis Born approximation S-matrix
    resonances.
    Interaction of quantum system with electromagnetic radiation: Longwave
    approximation selection rules for emission and absorption, quantum multipole
    expansion.
    Relativistic wave equations: Klein-Gordon equation, Dirac equation, continuity
    equation, interaction with electromagnetic field, non-relativistic limit,
    spin and intrinsic magnetic moment of Dirac particle.
    Utilization of groups in Quantum Mechanics: Operation of symmetry symmetries
    and conservation laws.
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
Teacher's information
* attendance in lectures and tutorials, active participation
and/or self-study of selected parts of recommended literature (homeworks)
* a few short written tests during semester (success rate 50 %)
* written and oral exam
The course is also listed under the following terms Winter 2000, Summer 2001, Winter 2001, Summer 2002, Winter 2002, Summer 2003, Winter 2003, Summer 2004, Winter 2004, Summer 2005, Winter 2006, Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, Summer 2011, Winter 2011, Summer 2012, Winter 2012, Summer 2013, Summer 2014.
  • Enrolment Statistics (Winter 2013, recent)
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