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Spectral Sum Rules for the Circular Aharonov‐Bohm Quantum Billiard
Author(s) -
Steiner F.
Publication year - 1987
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190350105
Subject(s) - dynamical billiards , convergence (economics) , physics , function (biology) , angular momentum , quantum , riemann zeta function , quantum mechanics , quantum superposition , classical mechanics , mathematics , mathematical analysis , evolutionary biology , economics , biology , economic growth
This work presents the results of a quantitative investigation of the “sum rule method” recently proposed by the author for calculating low‐lying energy levels. The system considered in detail is the circular Aharonov‐Bohm quantum billiard recently introduced by Berry and Robnik. Exact, expressions are derived for the spectral zeta function at positiveinteger values as a function of the magnetic flux. Using the zeta function for fixed angular momentum, we observe a very fast convergence to the exact ground state energy (“precocious convergence”).