COURSE GOALS: Through this Quantum Physics course, students should master the basic concepts of quantum mechanics and thoroughly understand functioning of some simple quantum systems. Students should also become familiar with descriptions and explanations of some more complicated quantum systems, albeit only on the level of qualitative understanding.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
1. KNOWLEDGE AND UNDERSTANDING
1.1. demonstrate a thorough knowledge and understanding of the fundamental laws of classical and modern physics;
1.2. demonstrate a thorough knowledge and understanding of the most important physics theories (logical and mathematical structure, experimental support, described physical phenomena);
1.8. demonstrate knowledge and understanding of new insights into contemporary physics and informatics teaching methods and strategies;
1.9. describe the framework of natural sciences;
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.1. identify and describe important aspects of a particular physical phenomenon or problem;
2.2. recognize and follow the logic of arguments, evaluate the adequacy of arguments and construct well supported arguments;
2.3. use mathematical methods to solve standard physics problems;
2.4. prepare and perform classroom physics experiments and interpret the results of observation;
3. MAKING JUDGMENTS
3.1. develop a critical scientific attitude towards research in general, and in particular by learning to critically evaluate arguments, assumptions, abstract concepts and data;
4. COMMUNICATION SKILLS
4.1. communicate effectively with pupils and colleagues;
4.2. present complex ideas clearly and concisely;
4.4. use the written and oral English language communication skills that are essential for pursuing a career in physics, informatics and education;
5. LEARNING SKILLS
5.1. search for and use professional literature as well as any other sources of relevant information;
5.3. develop a personal sense of responsibility for their professional advancement and development;
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
Upon completing the Quantum Physics course (including passing the exams), a student will be able to:
1. Give an overview of the historical context, i.e., the state of knowledge in physical sciences in the end of 19th and the beginning of 20th century, especially of those experimental results which indicated the inadequacy of classical physics and the need for new, quantum physics.
*Explain the need for introducing quanta of energy and quanta of light (photons) through the examples of blackbody radiation, photoelectric effect and Compton Effect.
*Explain the dual, particle-wave nature of photons, and its extension to the particle-wave nature of matter in general.
*Discuss critically the Bohr model of the hydrogen atom and its application to the hydrogen spectrum, and explain the link with de Broglie's hypothesis about the wave nature of micro-particles.
2. Explain how the wave-particle duality mandates that the associated wave function has the meaning of a probability amplitude. Explain the probabilistic character of quantum physics where Heisenberg uncertainty relations hold, as opposed to the determinism of classical physics.
*State, explain and apply the postulates of quantum mechanics as a theory of the new type.
*Use the basics of the formalism of wave mechanics, operators, eigenfunctions and eigenvalues for formulating the time-dependent and time-independent Schrödinger equations for wave functions of quantum states.
3. Explain the superposition principle in quantum mechanics, the concept of compatible and complementary observables. Explain the description of a physical system through a complete set of commuting operators.
4. Define not only basic operators, such as those of energy and momentum, but also more complicated ones, like the angular momentum operator. Solve Schrödinger equations for some simple and important cases: for a free particle, for the simplest bound and scattering states (with simplified interactions), for the harmonic oscillator, and for the hydrogen atom as well as similar systems (positronium and one-electron ions).
5. Explain qualitatively some properties of more complicated quantum systems, like molecules and multi-electron atoms assuming some general principles, such as Pauli Exclusion Principle for fermions. Describe the spin angular momentum in an intuitive, model way, and know about the connection between spin and statistics of fermions and bosons.
Rough division in fifteen lectures:
1. A conceptual and historic introduction.
2. Quantum of energy, and photon - the quantum of light. Blackbody radiation, derivation of Planck's formula, the photoelectric effect, the Compton Effect, the dual particle-wave nature of photons.
3. and 4. The dual, particle-wave nature of matter, and waves of probability. The Bohr model of the hydrogen atom. De Broglie hypothesis on the wave nature of micro-particles and its confirmation by Davison-Germer experiment. The Born interpretation of the quantum state wave function as a probability amplitude. Probabilistic character of quantum physics as opposed to classical determinism. Heisenberg uncertainty relations.
5. Some elements of the wave formalism and motivation for the postulates of quantum mechanics.
6. Postulates of quantum mechanics. Operators, eigenfunctions and eigenvalues. Illustrations by simple examples.
7. The simplest bound state. Elements of mathematical formalism. Schrödinger equation for a particle in an infinitely deep square potential well.
8. The superposition principle in quantum mechanics.
9. Commuting and non-commuting operators and compatible versus complementary observables.
10. Time evolution, conservation theorems, and symmetries including parity.
11. More complicated one-dimensional problems for bound and unbound states. Harmonic oscillator. Scattering in one dimension. Tunneling. One-dimensional square well of finite depth: bound states and their energies.
12. Transition to systems with more than one degrees of freedom: systems with more than one particle, and systems with more than one space dimension. Symmetric and antisymmetric two-particle wave functions.
13. Transition to three space dimensions and introduction of (orbital) angular momentum. Introduction of spin angular momentum in an intuitive way. Fermions and bosons, comments on the connection between spin and statistics of quantum objects.
14. Hydrogen atom and similar systems.
15. The Pauli principle and a qualitative description of more complicated atomic and molecular systems.
Corresponding exercises follow the above lectures in fifteen two-hour sessions.
REQUIREMENTS FOR STUDENTS:
Obligatory attendance of lectures and exercises
GRADING AND ASSESSING THE WORK OF STUDENTS:
Examination consists of written and oral parts.
- D. Klabučar, "Kvantni start", EXP EDIT, 2005.
- D. Klabučar, skripta ''Kraj početka: put prema zreloj kvantnoj teoriji''
- D. Klabučar, skripta ''Teorijskom sintezom prema postulatima kvantne mehanike''
- R. L. Liboff, "Introductory Quantum Mechanics", fourth edition, Pearson education Inc. publishing as Addison-Wesley, 2003
- F. S. Levin, "An introduction to Quantum Theory", Cambridge University Press, 2002.
- R. Eisberg and R. Resnick, "Quantum Physicsof Atoms, Molecules and Solids, Nuclei and Particles", John Wiley and Sons, 1985.