Course programme: 1. Introductory notes and course policies, motivation, main features of the quantum mechanics. Important experiments: Planck radiation law, photoeffect, Compton scattering, doublesplit experiment, emission spectra of atoms, FranckHertz experiment. Limits of the classical description of matter, boundary between classical and quantum physics. 2. Basics of mathematics and physics. Phase space in classical and quantum physics, Hilbert space, basis of vector space, norm, normalization, periodic functions in complex space, plane wave, orthonormality, operators in the state space, hermitian operators, spectrum of operators, matrix representation of operators in finitedimensional vector spaces, transformation of coordinates, spherical coordinates, determinant, etc. Examples. 3. De Broglie hypothesis, wave function, Schrödinger equation, interpretation of the wave function. 4. Description of properties a quantum particle. Operators of velocity and position of a quantum particle. Correspondence principle. Eigenstates and spectra of operators, their physical meaning. 5. Quantum particle in a potential well. Onedimensional classical harmonic oscillator, quantum particle in a harmonic potential, eigenstates, link between classical and quantum oscillator. Threedimensional harmonic oscillator. 6. State of a quantum system, complete set of observables. Operator of angular momentum. Quantum particle in a symmetric potential. Special case of harmonic and Coulomb potential. 7. Hydrogen, emission spectrum of hydrogen. Tunneling. Recapitulation of presented topics. 8. Measurement of physical quantities, Heisenberg uncertainty principles, consequences. 9. Timedependent Schrödinger equation, equation of continuity, development of a quantum particle, integrals of motion, Ehrenfest theorem. 10. SternGerlach experiment. A Quantum particle in a homogeneous magnetic field. Spin. 11. Systems of multiple particles, distinguishable particles, indistinguishable particles. Pauli principle. 12. Structure of atoms, Mendelejev's periodic table of the chemical elements. 13. Gentle introduction to a quantum physics of solids. Band structure. Bonds in solids, covalent bonding. 14. Technologically important applications of quantum physics. Summary of topics. Preparation for the exams. Practise: Directly related to the lectures. Meaning and consequences of principles, axioms, and derived relations are demonstrated on carefully chosen and easily solvable examples.


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