Quantum Mechanical Analysis of the Equilateral Triangle Billiard: Periodic Orbit Theory and Wave Packet Revivals
✍ Scribed by M.A. Doncheski; R.W. Robinett
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 286 KB
- Volume
- 299
- Category
- Article
- ISSN
- 0003-4916
No coin nor oath required. For personal study only.
✦ Synopsis
Using the fact that the energy eigenstates of the equilateral triangle infinite well (or billiard) are available in closed form, we examine the connections between the energy eigenvalue spectrum and the classical closed paths in this geometry, using both periodic orbit theory and the short-term semiclassical behavior of wave packets. We also discuss wave packet revivals and show that there are exact revivals, for all wave packets, at times given by T rev = 9µa 2 /4hπ where a and µ are the length of one side and the mass of the point particle, respectively. We find additional cases of exact revivals with shorter revival times for zero-momentum wave packets initially located at special symmetry points inside the billiard. Finally, we discuss simple variations on the equilateral (60 • -60 • -60 • ) triangle, such as the half equilateral (30 • -60 • -90 • ) triangle and other "foldings," which have related energy spectra and revival structures.