Computing quantum bound states on triply punctured two-sphere surface
We are interested in a quantum mechanical system on a triply punctured two-sphere surface with hyperbolic metric. The bound states on this system are described by the Maass cusp forms (MCFs) which are smooth square integrable eigenfunctions of the hyperbolic Laplacian. Their discrete eigenvalues and...
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| Format: | Article |
| Language: | English |
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Institute of Physics Publishing
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/55354/ http://psasir.upm.edu.my/id/eprint/55354/1/Computing%20quantum%20bound%20states%20on%20triply%20punctured%20two-sphere%20surface.pdf |
| _version_ | 1848852779735449600 |
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| author | Chan, K. T. Zainuddin, H. Atan, K. A. M. Siddig, A. A. |
| author_facet | Chan, K. T. Zainuddin, H. Atan, K. A. M. Siddig, A. A. |
| author_sort | Chan, K. T. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We are interested in a quantum mechanical system on a triply punctured two-sphere surface with hyperbolic metric. The bound states on this system are described by the Maass cusp forms (MCFs) which are smooth square integrable eigenfunctions of the hyperbolic Laplacian. Their discrete eigenvalues and the MCF are not known analytically. We solve numerically using a modified Hejhal and Then algorithm, which is suitable to compute eigenvalues for a surface with more than one cusp. We report on the computational results of some lower-lying eigenvalues for the triply punctured surface as well as providing plots of the MCF using GridMathematica. |
| first_indexed | 2025-11-15T10:43:30Z |
| format | Article |
| id | upm-55354 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:43:30Z |
| publishDate | 2016 |
| publisher | Institute of Physics Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-553542017-11-06T13:24:02Z http://psasir.upm.edu.my/id/eprint/55354/ Computing quantum bound states on triply punctured two-sphere surface Chan, K. T. Zainuddin, H. Atan, K. A. M. Siddig, A. A. We are interested in a quantum mechanical system on a triply punctured two-sphere surface with hyperbolic metric. The bound states on this system are described by the Maass cusp forms (MCFs) which are smooth square integrable eigenfunctions of the hyperbolic Laplacian. Their discrete eigenvalues and the MCF are not known analytically. We solve numerically using a modified Hejhal and Then algorithm, which is suitable to compute eigenvalues for a surface with more than one cusp. We report on the computational results of some lower-lying eigenvalues for the triply punctured surface as well as providing plots of the MCF using GridMathematica. Institute of Physics Publishing 2016 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/55354/1/Computing%20quantum%20bound%20states%20on%20triply%20punctured%20two-sphere%20surface.pdf Chan, K. T. and Zainuddin, H. and Atan, K. A. M. and Siddig, A. A. (2016) Computing quantum bound states on triply punctured two-sphere surface. Chinese Physics Letters, 33 (9). pp. 1-4. ISSN 0256-307X; ESSN: 1741-3540 10.1088/0256-307X/33/9/090301 |
| spellingShingle | Chan, K. T. Zainuddin, H. Atan, K. A. M. Siddig, A. A. Computing quantum bound states on triply punctured two-sphere surface |
| title | Computing quantum bound states on triply punctured two-sphere surface |
| title_full | Computing quantum bound states on triply punctured two-sphere surface |
| title_fullStr | Computing quantum bound states on triply punctured two-sphere surface |
| title_full_unstemmed | Computing quantum bound states on triply punctured two-sphere surface |
| title_short | Computing quantum bound states on triply punctured two-sphere surface |
| title_sort | computing quantum bound states on triply punctured two-sphere surface |
| url | http://psasir.upm.edu.my/id/eprint/55354/ http://psasir.upm.edu.my/id/eprint/55354/ http://psasir.upm.edu.my/id/eprint/55354/1/Computing%20quantum%20bound%20states%20on%20triply%20punctured%20two-sphere%20surface.pdf |