Eigenfunctions on a Stadium Associated with Avoided Crossings of Energy Levels
نویسندگان
چکیده
The most primitive form of a stadium is a circle, say of radius r. If we separate the left and right halves of the circle slightly and connect these two semi circles at the top and bottom by straight lines we have a classical stadium (racetrack). Let a be the horizontal distance from the center of the figure to either the left or right semi circle; that is, the distance of each ‘straightaway’ is 2a.
منابع مشابه
Quantum Chaos and Spectral Transitions in the Kicked Harper Model
In contrast to bounded systems, quantum chaos in extended systems may be associated with fractal spectra, metal-insulator transitions due to avoided band crossings, and spreading wave packets. In this lecture we point out the role of avoided band crossings for spectral transitions in the example of the kicked Harper model. We explain the coexistence of localized and extended eigenfunctions oo t...
متن کاملChaos in the Stadium Quantum Billiards
An expansion method was used to write a MATHEMATICA program to compute the energy levels and eigenfunctions of a 2-D quantum billiard system with arbitrary shape and dirichlet boundary conditions. One integrable system, the full circle, and one non-integrable system, the stadium, were examined. Chaotic properties were sought in nearest-neighbor energy level spacing distributions (NND). It was o...
متن کاملNon–Adiabatic Transitions near Avoided Crossings: Theory and Numerics
We present a review of rigorous mathematical results about non– adiabatic transitions in molecular systems that are associated with avoided crossings of electron energy level surfaces. We then present a novel numerical technique for studying these transitions that is based on expansions in semiclassical wavepackets.
متن کاملMolecular propagation through crossings and avoided crossings of electron energy levels
The time–dependent Born–Oppenheimer approximation describes the quantum mechanical motion of molecular systems. This approximation fails if a wavepacket propagates through an electron energy level crossing or “avoided crossing.” We discuss the various types of crossings and avoided crossings and describe what happens when molecular systems propagate through them. It is not practical to solve th...
متن کاملQuantum Chaos: An Exploration of the Stadium Billiard Using Finite Differences
We investigate quantum chaos in chaotic billiards by modelling the square (non-chaotic) and the stadium (chaotic) billiards as 2D infinite square wells. We developed MATLAB code that uses grid points and the method of finite differences to numerically solve the Schrödinger equation for either case. We successfully obtained the “scar” structures in higher energy eigenfunctions for the stadium ca...
متن کامل