COURSE GOALS: The principal objectives of the course Quantum Physics are the introduction of basic concepts and methods of nonrelativistic quantum mechanics, further development of acquired mathematical skills and their applications to selected physical problems, and the preparation of students for more advanced courses in theoretical physics and specialized courses in atomic, solid-state, particle and nuclear physics.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
Upon completing the degree, students will be able to:
1. KNOWLEDGE AND UNDERSTANDING
1.2 demonstrate a thorough knowledge of advanced methods of theoretical physics including classical mechanics, classical electrodynamics, statistical physics and quantum physics
1.3 demonstrate a thorough knowledge of the most important physics theories (logical and mathematical structure, experimental support, described physical phenomena)
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.1 identify the essentials of a process/situation and set up a working model of the same or recognize and use the existing models
2.3 apply standard methods of mathematical physics, in particular mathematical analysis and linear algebra and corresponding numerical methods
2.5 perform numerical calculation independently, even when a small personal computer or a large computer is needed, including the development of simple software programs
4. COMMUNICATION SKILLS
4.3 develop the written and oral English language communication skills that are essential for pursuing a career in physics
5. LEARNING SKILLS
5.1 search for and use physical and other technical literature, as well as any other sources of information relevant to research work and technical project development (good knowledge of technical English is required)
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
Upon completing the course Quantum Physics, students will be able to:
- formulate and apply basic concepts and features of quantum mechanics (principles of superposition and complementarity, Hilbert space of state vectors, observables), explain the relation between abstract concepts such as projectors, expectation values, etc. and their experimental realizations
- describe basic properties of the Schrödinger equation and wave function, explain the relation between the coordinate and impulse representations, understand the concept of different pictures of quantum mechanics (Schrödinger, Heisenberg and Dirac)
- apply commutators, derive the uncertainty relations and explain their experimental consequences
- solve the time-independent Schrödinger equation for bound and scattering states in one, two and three dimensions, interpret the resulting wave function and calculate expectation values for various observables
- solve the time-dependent Schrödinger equation for a wave packet in an arbitrary one- dimensional potential, interpret the resulting wave function and calculate the expectation values for various observables
- explain the relation between the operator of rotation and the orbital angular momentum, calculate the eigenvalues and eigenfunctions of orbital angular momentum, and apply the algebra of orbital angular momentum in practical problems
- explain the concept of spin, calculate the eigenvalues and the eigenfunctions of the spin operator, apply the algebra of spin operators in practical problems, couple spin and orbital angular momenta
- properly (anti)symmetrize the wave function for idential particles, explain the relation between the spin and statistics of a particle (Bose-Einstein or Fermi-Dirac)
- discuss the concept of symmetries and conservation laws (Noether's theorem) in the context of quantum mechanics
- apply approximate methods (the variational method, time-independent perturbation theory, time-dependent perturbation theory) to solve perturbation problems in quantum mechanics
- solve simple atomic and molecular problems - hydrogen and helium atom, and the hydrogen molecular ion
- describe the basic concepts of quantum optics, including a simple quantization of the electromagnetic field; Fock, coherent and squeezed states; and the Jaynes-Cunnings model
- calculate expectation values of various observables in the Fock, coherent and squeezed state
- describe the basic concepts of entanglement and non-separability, the Einstein-Podolsky-Rosen argument, the theory of hidden variables and Bell inequalities.
- From classical to quantum mechanics.
- Quantum observables and states.
- Quantum dynamics.
- Harmonic oscillator in quantum mechanics.
- Density matrix.
- Angular momentum and spin.
- Identical particles.
- Symmetries and conservation laws.
- The measurement problem in quantum mechanics.
- Approximate methods (stationary and time-dependent perturbation theory, variational method).
- Elementary scattering theory.
- Hydrogen and helium atoms.
- Hydrogen molecular ion, vibrational and rotational degrees of freedom.
- Quantum optics.
- Entanglement and non-separability.
- Quantum information and computation.
REQUIREMENTS FOR STUDENTS:
Students are required to regularly attend classes, participate actively in solving problems and write a seminar paper in each semester. Furthermore, students are required to pass two written examinations, one at the end of winter semester and one at the end of the summer semester.
GRADING AND ASSESSING THE WORK OF STUDENTS:
At the end of the course an oral exam is held for students who have successfully completed the requirements of the course.
- G. Auletta, Mauro Fortunato, G. Parisi : Quantum Mechanics, Cambridge University Press, 2009
- M. LeBellac: Quantum Physics, Cambridge University Press, 2006
R. Shankar: Principles of Quantum Mechanics, Springer Science+Bussines Media, 1994 (second edition)