## List of questions (problems)

During the qualification talk the candidate will draw a problem from the given list.
However, the problem may be specified more precisely, according to the candidates
interests, education and intentions to participate in one of the subprojects.
The more precise, specified questions are listed in the **"key problems for prepartion
to qualification (recruitment) procedure"** attached to the descriptions of each of
the subprojects. They may be more specific and elucidating the more general ones.

- Wave-corpuscular duality in quantum mechanics.
- Postulates of quantum mechanics.
- The role of the Schroedinger equation and its fundamental consequences.
- Fundamentals of the mathematical formalism of quantum mechanics.
- Measurement in quantum versus classical mechanics.
- Heisenberg and time-energy uncertainty relations.
- Time evolution in quantum mechanics. Schroedinger, Heisenberg and interaction pictures.
- Harmonic oscillator in position and energy representations.
- Angular momentum in quantum mechanics.
- Schroedinger theory of the hydrogen-like atom.
- Interaction with electromagnetic fields in quantum mechanics. Fundamentals and examples.
- Stationary perturbation theory.
- Time-dependent perturbation theory.
- Density operator. Fundamental concepts and properties.
- The concept of entanglement — main issues.
- Spin 1/2. Pauli equation.
- Adiabatic approximation in solid state and molecular physics.
- Energetic electronic structure of crystals.
- Concept of phonons.
- Concept of exciton.
- Concept of hole in valence band.
- Concept of Cooper pair.
- Energetic structure of related to transition metal and rare earth ions in crystals.