Enrollement status.

Final examination pending on succesfully completed numerical exercises.

# Quantum mechanics

Schroedinger equation: Properties of the Schroedinger equation and the wave function for one particle. Symmetries: parity, time reversal, rotations, translations.

Operators: Introduction of operators and expectation values for the probability density, current, velocity, momentum, acceleration. Classical limit.

Formalism of quantum mechanics: Postulates of quantum mechanics. Matrix formulation. Connection between the wave function and the Dirac formalism: p- and r- representations. Time evolution operator. Operator and eigenfunctions of orbital angular momentum.

Examples: Application of the formalism in special cases: wave packet, harmonic oscillator and coherent state, spherical symmetric problems, electron in magnetic field. Relation to classical mechanics.

Spin: Formalism for spin and angular momentum. Pauli matrices. Non-locality of quantum mechanics.

Perturbation theory: The first and the second order for non-degenerate spectrum. The first order for degenerate spectrum. Time dependent perturbation. Fermi golden rule. Examples.

Scattering of particles and the scattering matrix.

F. Schwabl, Quantum Mechanics. Springer-Lehrbuch, Heidelberg, 2002.

J. J. Sakurai, Modern Quantum Mechanics. Addison Wesley Longman, 1994.

E. Merzbacher, Quantum Mechanics. John Wiley & Sons, New York, 1970.

L.D. Landau, E.M. Lifshitz, Quantum Mechanics. Pergamon Press Ltd., London, 1958.

Objectives: Understanding of similarities between classical and quantum mechanics. Understanding of quantized quantities in nature. Ability to formulate and to solve related single electron problems.

Acquired competence:

Theoretical understanding.

Modeling and solving the models of physical systems.

In depth knowledge of the quantum mechanics.

Acquired capacity to do independent literature search.

Knowledge and understanding

Knowledge of the principles of quantum probability.

Competences

Learn the line spectrum of light, wave properties of particles, spin of the electron.

Reflection

Abstract modeling of physical systems.

Portable competences – not connected with a single subject

The basic knowledge for the understanding of microscopic effects: condensed matter physics, atoms, molecules, nucleai and elementary particles.

Lectures, numerical exercices, homeworks and consultations.

2 tests on numerical exercises or a written examination

Oral examination

grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

- A non-adiabatically driven electron in a quantum wire with spin-orbit

interaction, T. Čadež, J.H. Jefferson, and A. Ramšak, New J. Phys. 15, 013029

(2013). - Geometric analysis of entangled qubit pairs, A. Ramšak, New J. Phys. 13,

103037 (2011). - Geometrical view of quantum entanglement, A. Ramšak, Europhys. Lett. 96,

40004 (2011). - Spin qubits in double quantum dots - entanglement versus the Kondo effect,

A. Ramšak, J. Mravlje, R. Žitko, and J. Bonča, Phys. Rev. B 74, 241305(R)

(2006). - Entanglement of two delocalized electrons, A. Ramšak, I. Sega, and J.H.

Jefferson, Phys. Rev. A 74, 010304(R) (2006).