Syllabus
(1) Introduction. The aim and scope of quantum mechanics (QM). Failure of classical physics as an origin of QM. Experiments leading to QM. Evolution of conceptions of microscopic particles and light. Characteristic features of microscopic systems: quantisation of physical observables, wave nature of particles, uncertainty relations, specificities of measurements in QM. (2) Basic postulates and formalism of QM. Description of quantum state. Wave function, its properties and interpretation. Normalization. Superposition principle, its interpretation and consequences. Vector space of quantum states. Scalar product. Physical observables. Linear and hermitian operators. Operators of physical observables, its construction, correspondence principle. Commutation relations. Expectation values, eigenvalues and eigenfunctions of operators of physical observables. Measurement in QM. Schrödinger (nonstationary and stationary) equation. Continuity equation. Flux density. Time evolution and conservation laws. Energy levels. Integrals of motion. Quantum equations of motion. Ehrenfest theorems. Relation between classical and quantum physics. (3) Selected applications. Particle in rectangular potential box. Potential step. Potential barrier, tunnelling. Harmonic oscillator, atomic oscillation in crystals, normal modes. Free particle. (4) Angular momentum. Particle in central field. Separation of coordinates and solution of multi-dimensional problems. Hydrogen atom. (5) Spin. Experimental discovery of spin. Spin function. Spin operators. Pauli matrices. Pauli equation. Zeeman effect. (6) Approximate methods of QM. Stationary perturbation theory for nondegenerate and degenerate energy levels. Nonstationary perturbation theory and quantum transitions. Variation methods. Selected applications. (7) Many-particle systems. Extension of QM postulates for many-particle systems. Specificities of systems of identical particles. Indistinguishability principle and its consequences. Pauli principle. Periodic table. Adiabatic approximation, separation of electron and nuclear coordinates. Hydrogen atom as a two-particle problem. Helium. (8) Chemical bond. Quantum explanation of chemical bond. Spin component of two particle wavefunction. Hydrogen molecule.
Annotation
Lecture of fundamentals of quantum mechanics for future physics teachers.