Quantum mechanics 2

Dr. Irina Petreska, Professor

Course content:  

Quasirelativistic quantum mechanics. Klein-Gordon equation. Dirac equation. Relativistic corrections. Spectrum of a hydrogen atom in a magnetic field.

A system of many particles. Introduction. Identical particles, principle of indistinguishability. A system of two identical particles. Law of conservation of symmetry. Bosons. Fermions. A system of N identical particles. Many-electron systems. Matrix elements. Self-aligned field. Hartree-Fock method. Functional of the electron density. Hohenberg-Cohn theorems. Kohn-Shem equations. Secondary quantization. Annihilation and generation operator.

Many-electron atoms. Electronic configuration. Atomic spectral terms. Corrections to electronic terms. Spin-orbit interaction. Fine structure. An atom in a homogeneous magnetic field. An atom in a homogeneous electric field. Two-electron atoms. Statistical models.

Radiation theory. Semiclassical radiation theory. Transition probability within non-stationary perturbation theory. Multiple Decomposition. Dipole approximation. Einstein coefficients. Choice rules in dipole approximation. Characteristics of radiation – lifetime, intensity and natural width of spectral lines. Atomic spectra.

Theory of scattering. Introduction and definitions. Types of scattering. Elastic collisions. Lippmann-Schwinger equation. Calculation of the differential effective cross-section and the amplitude of the scattered packet. Optical theorem. Born approximation. Centrally symmetric problems and partial wave method. A time-dependent formulation of the scattering problem. Inelastic collisions. Electron scattering from a hydrogen-like atom. Inelastic scattering – partial wave method. Total effective scattering cross section.

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