COURSE GOALS: The principal objectives of the course are to introduce basic concepts and postulates of quantum physics, develop the necessary mathematical skills and apply them to simple quantum mechanical problems, and prepare the students for the course Quantum physics that follows in the third year.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
Upon completing the degree, students will be able to:
1. KNOWLEDGE AND UNDERSTANDING
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
2.2 evaluate clearly the orders of magnitude in situations which are physically different, but show analogies, thus allowing the use of known solutions in new problems;
2.3 apply standard methods of mathematical physics, in particular mathematical analysis and linear algebra and corresponding numerical methods
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 Introduction to Quantum Physics, students will be able to:
* discuss the problems of classical physics that have led to the development of quantum physics - black body radiation, photoelectrical effect, interference and the Bohr atomic model
* apply basic mathematical concepts to simple finite-dimensional quantum systems
* analyze fundamental concepts of quantum mechanics based on simple examples such as the polarization of light and spin 1 systems
* discuss the postulates of quantum physics - the superposition principle, wave function collapse and the Heisenberg inequality relations
* describe the time evolution of a quantum system and apply the concept to illustrative finite dimensional systems
* utilize quantum mechanical concepts for a description of selected examples such as , for instance, molecules and nuclear magnetic resonance
* describe the concept of entanglement and the role of the density operator.
COURSE DESCRIPTION:
* Structure of matter, basic interactions, classical and quantum physics
* Beginnings of quantum theory, black body radiation - thermodynamical analysis, UV divergence and the quantization of energy, photoelectrical effect - the Millikan experiment and the Einstein hypothesis
* waves and particles, de Broglie postulate, diffraction and interference of cold neutrons, two slits experiment and the interpretation, energy in classical and quantum physics
* Bohr atomic model, finitedimensional Hilbert space, linear, Hermitian and unitary operators, projectors
* diagonalization of Hermitian operators, eigenvalues, eigenvectors and their properties, illustrative example using a 2x2 matrix, complete set of compatible operators and the commutator, operator functions
* polarization of EM waves, linear and circular polarization and the unitary transformation between the bases
* angular momentum and magnetic moment in classical physics, Stern-Gerlach experiment, projection of spin on an arbitrary axis, rotation of spin, Pauli matrices and the commutation relations
* principle of superposition, probability amplitude and the Born rule, operators and physical properties, operator expectation value, wave function collapse
* Heisenberg inequality relations, dispersion of an observable, time evolution of a quantum system - evolution operator, stationary states, case of the time-independent Hamiltonian
* temporal Heisenberg inequality, Schrödinger and Heisenberg picture, ethylene and benzene molecules
* resonances, two state atom, EM interaction, spontaneous and stimulated emission
* product of two vector spaces, dimension and basis of the product space, system of two 1 spins
* density operator - definition and properties, operator expectation value, density operator for a system with two states
REQUIREMENTS FOR STUDENTS:
Students are required to regularly attend classes and participate actively in solving problems.
GRADING AND ASSESSING THE WORK OF STUDENTS:
At the end of the course a written and oral examination is held for students who have successfully completed the requirements of the course.
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