Syllabus
1. What is it a quantum mechanics (QM). Experimental sources of QM. Charakteristic features of microscopic systems: quantization of physical observables, quantum properties of light, wave behaviour of particles (wave-particle duality), uncertainty relations, the key-role of measurement in QM, statistical nature of QM. The relation of quantum physics to classical physics. Energy-frequency and momentum-wavelength relations for photon. De Broglie's hypothesis and wave charakteristics of particles.
2. The concept of quantum state. Wave function - its properties and statistical interpretation. Probability density of particle position. Normalization condition. Principle of superposition of qantum states. Wavepacket.
3. Operators in QM. Linear and hermitian operators. Basic mathematical operations with operators. Operators of physical observables. Operators of particle position, momentum, angular momentum, kinetic energy and potential energy. Hamilton operator (hamiltonian). Commutation relations. The interpretation of eigenvalues and eigenfunctions of operators. Mean values of physical observables. Elementary description of experiment in QM. Simultaneous measurability of physical observables. Uncertainty relations.
4. Time evolution of quantum state. Nonstationary Schrödinger equation. Stationary Schrödinger equation. Stationary and nonstationary quantum states. Simple applications: Free particle. Particle in potential box. Penetration of particle through potential barrier (tunnelling). Linear harmonic oscillator. Rigid rotor.
5. Particle in central potential. Orbital angular momentum. Quantum numbers l, m. Schrödinger equation for hydrogen atom. Radial and angular components of wavefunctions. Atomic energy levels of hydrogen. Stern-Gerlach experiment and spin. Significance of spin.
6. Extensions of QM to many-particle systems. Separation of electronic and nuclear motions in molecule (adiabatic approximation). Systems of identical particles. Principle of particle identity. Symmetric and antisymmetric wavefunctions. Bosons and fermions. One-particle approximation. Pauli principle. Elementary QM-clarification of chemical bond. Hydrogen molecule. Molecular vibrations and rotations.
Annotation
An introduction to quantum mechanics (QM) for students of chemistry. Physical principles of QM and its typical applications.
Characteristic features of microscopic systems: the quantization of energy and the other observables, the wave charakter of particles, the uncertainty principle, the importance of the measurement. The selected topics: the description of quantum states, the operator treatment of physical observables, Schrödinger equation, the elementary introduction to QM of many-partical systems, the QM-clarification of the chemical bond.
The relation of QM to classical mechanics.