Quantum bound states on some hyperbolic surfaces
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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Institute of Physics Publishing
2017
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| Online Access: | http://psasir.upm.edu.my/id/eprint/54587/1/Quantum%20bound%20states%20on%20some%20hyperbolic%20surfaces.pdf |
| _version_ | 1796976112384868352 |
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| author | Zainuddin, Hishamuddin Kar Tim, Chan Shamsuddin, Nor Syazana Mohd Shah, Nurisya |
| author_facet | Zainuddin, Hishamuddin Kar Tim, Chan Shamsuddin, Nor Syazana Mohd Shah, Nurisya |
| author_sort | Zainuddin, Hishamuddin |
| collection | UPM |
| description | 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. |
| first_indexed | 2024-03-06T09:21:07Z |
| format | Article |
| id | upm.eprints-54587 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:21:07Z |
| publishDate | 2017 |
| publisher | Institute of Physics Publishing |
| record_format | dspace |
| spelling | upm.eprints-545872020-03-17T06:57:06Z http://psasir.upm.edu.my/id/eprint/54587/ Quantum bound states on some hyperbolic surfaces Zainuddin, Hishamuddin Kar Tim, Chan Shamsuddin, Nor Syazana Mohd Shah, Nurisya 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. Institute of Physics Publishing 2017 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/54587/1/Quantum%20bound%20states%20on%20some%20hyperbolic%20surfaces.pdf 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 https://iopscience.iop.org/article/10.1088/1742-6596/795/1/012002 1088/1742-6596/795/1/012002 |
| spellingShingle | Zainuddin, Hishamuddin Kar Tim, Chan Shamsuddin, Nor Syazana Mohd Shah, Nurisya Quantum bound states on some hyperbolic surfaces |
| title | Quantum bound states on some hyperbolic surfaces |
| title_full | Quantum bound states on some hyperbolic surfaces |
| title_fullStr | Quantum bound states on some hyperbolic surfaces |
| title_full_unstemmed | Quantum bound states on some hyperbolic surfaces |
| title_short | Quantum bound states on some hyperbolic surfaces |
| title_sort | quantum bound states on some hyperbolic surfaces |
| url | http://psasir.upm.edu.my/id/eprint/54587/1/Quantum%20bound%20states%20on%20some%20hyperbolic%20surfaces.pdf |
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