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Quantum bound states on some hyperbolic surfaces


Citation

Zainuddin, Hishamuddin and Kar Tim, Chan and Shamsuddin, Nor Syazana and Mohd Shah, Nurisya (2017) Quantum bound states on some hyperbolic surfaces. Journal of Physics: Conference Series, 795. pp. 1-10. ISSN 1742-6588; ESSN: 1742-6596

Abstract

The aim of this work is to highlight results of energy eigenstates on some noncompact finite hyperbolic surfaces. Such systems are known to exhibit both continuous and discrete spectra and are dependent on the subgroups of the modular group that underlie these surfaces. We study explicitly the cases of Maass cusp forms on the singly punctured two-torus and the triply punctured two-sphere for their eigenvalues. The eigenvalues for the torus system are doubly degenerate while for the sphere case, the eigenvalues are nondegenerate. We also note that the lowest eigenvalue of the sphere system is larger than that of the torus system.


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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: 1088/1742-6596/795/1/012002
Publisher: Institute of Physics Publishing
Keywords: Hyperbolic surfaces; Energy eigenstates; Quantum versions; Quantum chaos
Depositing User: Nurul Ainie Mokhtar
Date Deposited: 17 Mar 2020 06:57
Last Modified: 17 Mar 2020 06:57
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=1088/1742-6596/795/1/012002
URI: http://psasir.upm.edu.my/id/eprint/54587
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