COURSE AIMS AND OBJECTIVES: Mastering the basic concepts of quantum mechanics, understanding basics of quantum physics and functioning of simple quantum systems. Qualitative and informative decriptions and explanations also of some more complicated quantum systems.
COURSE DESCRIPTION AND SYLLABUS:
- Introduction - conceptual and historical
- Quantum of energy, and photons - the quanta of light (electromagntic radiation) Blackbody radiation, derivation of Planck's formula. Photoelectric effect, Compton effect, the dual particle-wave nature of photons.
- Particle-wave nature of matter and probability waves The Bohr model of hydrogen atom. De Broglie hypothesis on the wave nature of micro-particles and its confirmation by the Davison-Germer experiment. The particle-wave duality of micro-particles and necessity of associating to them a wave function - a probability amplitude. The probabilistic character of quantum physics in contrast to classical determinism. Heisenberg uncertainty relations.
- Elements of wave formalism and motivations for the postulates of quantum mechanics
- The postulates of quantum mechanics. Operators, eigenfunctions and eigenvalues. Illustrations thereof by simple examples.
- The simplest bound state The needed elements of mathematical formalism. Schrödinger equation for a particle in the infinitely deep rectangular potential.
- Superposition principle in quantum mechanics
- Commutation properties of operators, and compatible vs. complementary observables
- Time evolution, conservation theorems and symmetries (including parity)
- More advanced one-dimensional problems for bound and unbound states Harmonic oscillator. Scattering on flat obstacles - a simple step and rectangular potential. Tunneling through the rectangular potential. A rectangular one-dimensional potential well of a finite depth: bound states and their energies.
- Transition to systems with more than one degree of freedom - i.e., multiparticle or multidimensional systems. Symmetric and antisymmetric two-particle wave functions.
- Transition to the three-dimensional space and introduction of angular momentum Introduction of spin in an intuitive way. Bosons and fermions, and some remarks concerning the connection between spin and statistics of quantum objects.
- Hydrogen atom and similar systems
- The Pauli priciple and qualitative description of more complicated atom and molecular systems.