Expansion method for stationary states of quantum billiards

American Journal of Physics

Volumn 67, Issue 2, 1999, Pages 133-141

  Kaufman, David L ^a   Kosztin, Ioan ^b   Schulten, Klaus ^c  

^a Bethel College Kansas   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

^c University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033471502     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.19208     Document Type: Article

References (11)

1. R. L. Liboff, Introductory Quantum Mechanics (Addison-Wesley, Reading, MA, 1998), 3rd ed.
2. For a recent review of some quantum and classical aspects of the circle billiard see, e.g., R. W. Robinet, "Visualizing the solutions for the circular infinite well in quantum and classical mechanics," Am. J. Phys. 64, 440-446 (1996).
3. For an overview of nanoelectronics see, e.g., F. A. Buot, "Mesoscopic physics and nanoelectronics: Nanoscience and nanotechnology," Phys. Rep. 234, 73-174 (1993).
4. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).
5. For an introduction to the physics of classical billiard systems see, e.g., M. V. Berry, "Regularity and chaos in classical mechanics, illustrated by three deformations of a circular 'billiard,' " Eur. J. Phys. 2, 91-102 (1981).
6. A. Kudrolli, V. Kidambi, and S. Sridhar, "Experimental Studies of Chaos and Localization in Quantum Wave Functions," Phys. Rev. Lett. 75, 822-825 (1995).
7. The MATHEMATICA3.0 notebook which contains a complete numerical implementation of the EM is freely available from one of the authors (K.S.).
8. M. L. Mehta, Random Matrices (Academic, Boston, 1990), 2nd ed.
9. I. Kosztin and K. Schulten, "Boundary Integral Method for Stationary States of Two-Dimensional Quantum Systems," Int. J. Mod. Phys. C 8, 293-325 (1997).
10. M. V. Berry and M. Wilkinson, "Diabolical points in the spectra of triangles," Proc. R. Soc. London, Ser. A 392, 15-43 (1984).
11. M. Tinkham, Group Theory and Quantum Mechanics (McGraw-Hill, New York, 1964).