Předmět Kvantová teorie a spektroskopie (UFY / KTS)

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Materiál	Typ	Datum	Počet stažení

Obsah

Content:Foundations of Quantum Mechanics. Black body radiation (Wien, Rayleigh-Jeans, Planck), photoelectric effect, Compton scattering, heat capacities of solids, two-slit experiment with electrons, de Broglie waves, wavepacket.Basics of QM. Wavefunstion, statistical interpretation, superposition of states, operators, mean values of coordinate and momentum, operators of coordinates, momentum, angular momentum, energy, commutators, eigenvalues and eigenfunctions.Uncertainty principle. Measurements in QM, properties of operator eingefunctions, simultaneous measurement of physical quantities, uncertainty principle (coordinate, momentum, angular momentum, energy), interaction of apparatus with microobjects.Schrödinger equation. Principal SR, Hamiltonian, stationary SR, basic principles for solution of SR (infinite potential well, particle in a box, degeneration of states, tunneling.Harmonic oscilátor in QM. Full solution of simple harmonic motion in QM, properties of solutions, properties of wavefunctions, concept of zero energy motion and its consequences.Particle in a central force field. Angular momentum in QM, movement in a field of spherical symmetry, Coulombic field, hydrogen atom - quantum statwes, quantum numbers, discrete energy spectrum, propertiers of wavefunctions, atomic orbitals.Spin. Experiments leading to a discovery of spin, multiplet structure of spectrum, splitting of energy levels in magnetic field, spin operators, Pauli matrices, Pauli equation, spin as relativistic effect, total angular momentum.Multielectron atoms. Set of identical particles, Pauli exclusion principle, Slater determinant, helium atom, periodic table.Introduction to chemical bond. Nature of chemical bond, ionic and covalent bond, valence and core electrons, - and -electrons, bond direction, hybridization.Representation theory. Heisenberg and Dirac representations of QM, matrix mechanics, braket Dirac notation, transformation of opertaors and wavefunctions between different representations.

Získané způsobilosti

Students acquire the ability to describe simple quantum effects and behaviour of micro-particles using introduction and mastering of necessary mathematical tools. Further more, the interaction of a light with a solid matter will be described, together with theoretical and experimental fundamentals of the absorption, emission, and light-scattering spectroscopies - conventional and laser ones. In corresponding exercises, the practical examples of simple quantum objects and their behaviour will be given and elucidated.

Literatura

Atkins, P.W., Friedman, R.S.: Molecular Quantum Mechanics. Landau, L. D., Lifshitz, E. M, Quantum Mechanics, Non-Relativistic Theory. Messiah, A.: Quantum Mechanics.

Požadavky

The prerequisite of a credit award shall be an active participation of the student in lectures and exercises. During the exam, the student should answer to 3 assigned questions concerning the covered subject-matter.

Garant

prof. RNDr. Tomáš Polívka, Ph.D.

Vyučující

prof. RNDr. Tomáš Polívka, Ph.D.prof. RNDr. Tomáš Polívka, Ph.D.