量子力學(一)

The course provides a deeper understanding of general phenomena in systems that behave essentially quantum mechanically and practical introductions to methods used to describe this behavior. The phenomena include the nature of the spectrum (discrete or continuous), scattering and tunneling. Several exactly solvable problems are presented: harmonic oscillator, electron in Coulomb potential, potential well,... and numerical method of approximate solution is introduced. Several applications are presented: the physics of angular momentum and spin and the theory of simple atoms and nuclei. Content A. Statistical description of a quantum particle by the wave function. 1. Wave function and its probablistic interpretation. 2. Schroedinger equation and distributions of coordinate and momentum. 3. Hilbert space of wave functions and representation of physical quantities as operators. B. Stationary states. Discrete vs continuum spectrum. 1. Probability flow. Spectra of the single particle Schroedinger equation. 2. Origin of the discrete spectrum. 3. Continuous spectrum in QM – just an idealization. C. Solvable 1D models. The tunneling phenomenon. 1. Harmonic oscillator. 2. Bound state in a well. 3. Integral transformation for the localized potentials. 4. Tunneling over a barrier. D. Discretization and numetical determination of the QM spectrum. 1. Tight binding models: 1D chain. 2. More than one dimension E. Symmetry, degeneracy and angular momentum. 1. 3D rotation invariant systems and degeneracy. 2. Use of 3D rotation symmetry. Discreteness of the angular momentum. 3. Spherical harmonics. 4. Coulomb interaction and atomic levels. F. Quantum dynamics. 1. Few solvable cases: small spin rotation to the Landau-Zener tunneling. 2. Coherent states of harmonic oscillator and the wave packet motion. 3. Adiabatic evolution and the Berry phase. 4. Simulation of the quantum evolution.

Introductory Quantum Mechanics

Grades cccording to exercises and works given in the class (see also pp). Each exercise carries 1 or 2 points, while the work (analytic or numerical) carries 2 to 4 points. Each student should present in class solution worth of cumulative 4 points.

A. Konishi and G. Paffuti, “Quantum Mechanics”, Oxford University Press, London (2009).