Abstract
For quantum problems on the pseudo-sphere generated by arithmetic groups there exist special trace formulae, called trace formulae for Hecke operators, which permit the reconstruction of wave functions from the knowledge of periodic orbits. After a short discussion of this subject, the Hecke operators trace formulae are presented for the Dirichlet problem on the modular billiard, which is a prototype of arithmetical systems. The results of numerical computations for these semiclassical type relations are in good agreement with the directly computed eigenfunctions. (author) 23 refs.; 2 figs.
Citation Formats
Bogomolny, E B, Georgeot, B, Giannoni, M J, and Schmit, C.
Trace formulae for arithmetical systems.
France: N. p.,
1992.
Web.
Bogomolny, E B, Georgeot, B, Giannoni, M J, & Schmit, C.
Trace formulae for arithmetical systems.
France.
Bogomolny, E B, Georgeot, B, Giannoni, M J, and Schmit, C.
1992.
"Trace formulae for arithmetical systems."
France.
@misc{etde_10109785,
title = {Trace formulae for arithmetical systems}
author = {Bogomolny, E B, Georgeot, B, Giannoni, M J, and Schmit, C}
abstractNote = {For quantum problems on the pseudo-sphere generated by arithmetic groups there exist special trace formulae, called trace formulae for Hecke operators, which permit the reconstruction of wave functions from the knowledge of periodic orbits. After a short discussion of this subject, the Hecke operators trace formulae are presented for the Dirichlet problem on the modular billiard, which is a prototype of arithmetical systems. The results of numerical computations for these semiclassical type relations are in good agreement with the directly computed eigenfunctions. (author) 23 refs.; 2 figs.}
place = {France}
year = {1992}
month = {Sep}
}
title = {Trace formulae for arithmetical systems}
author = {Bogomolny, E B, Georgeot, B, Giannoni, M J, and Schmit, C}
abstractNote = {For quantum problems on the pseudo-sphere generated by arithmetic groups there exist special trace formulae, called trace formulae for Hecke operators, which permit the reconstruction of wave functions from the knowledge of periodic orbits. After a short discussion of this subject, the Hecke operators trace formulae are presented for the Dirichlet problem on the modular billiard, which is a prototype of arithmetical systems. The results of numerical computations for these semiclassical type relations are in good agreement with the directly computed eigenfunctions. (author) 23 refs.; 2 figs.}
place = {France}
year = {1992}
month = {Sep}
}