Computation of quantum bound states on a singly punctured two-torus
We study a quantum mechanical system on a singly punctured two-torus with bound states described by the Maass waveforms which are eigenfunctions of the hyperbolic Laplace—Beltrami operator. Since the discrete eigenvalues of the Maass cusp form are not known analytically, they are solved numerically...
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| Format: | Article |
| Language: | English English |
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Institute of Physics
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30081/ http://psasir.upm.edu.my/id/eprint/30081/1/Computation%20of%20quantum%20bound%20states%20on%20a%20singly%20punctured%20two.pdf |
| _version_ | 1848846577134731264 |
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| author | Chan, Kar Tim Zainuddin, Hishamuddin Molladavoudi, Saeid |
| author_facet | Chan, Kar Tim Zainuddin, Hishamuddin Molladavoudi, Saeid |
| author_sort | Chan, Kar Tim |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We study a quantum mechanical system on a singly punctured two-torus with bound states described by the Maass waveforms which are eigenfunctions of the hyperbolic Laplace—Beltrami operator. Since the discrete eigenvalues of the Maass cusp form are not known analytically, they are solved numerically using an adapted algorithm of Hejhal and Then to compute Maass cusp forms on the punctured two-torus. We report on the computational results of the lower lying eigenvalues for the punctured two-torus and find that they are doubly-degenerate. We also visualize the eigenstates of selected eigenvalues using GridMathematica. |
| first_indexed | 2025-11-15T09:04:55Z |
| format | Article |
| id | upm-30081 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T09:04:55Z |
| publishDate | 2013 |
| publisher | Institute of Physics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-300812015-09-11T01:40:45Z http://psasir.upm.edu.my/id/eprint/30081/ Computation of quantum bound states on a singly punctured two-torus Chan, Kar Tim Zainuddin, Hishamuddin Molladavoudi, Saeid We study a quantum mechanical system on a singly punctured two-torus with bound states described by the Maass waveforms which are eigenfunctions of the hyperbolic Laplace—Beltrami operator. Since the discrete eigenvalues of the Maass cusp form are not known analytically, they are solved numerically using an adapted algorithm of Hejhal and Then to compute Maass cusp forms on the punctured two-torus. We report on the computational results of the lower lying eigenvalues for the punctured two-torus and find that they are doubly-degenerate. We also visualize the eigenstates of selected eigenvalues using GridMathematica. Institute of Physics 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30081/1/Computation%20of%20quantum%20bound%20states%20on%20a%20singly%20punctured%20two.pdf Chan, Kar Tim and Zainuddin, Hishamuddin and Molladavoudi, Saeid (2013) Computation of quantum bound states on a singly punctured two-torus. Chinese Physics Letters, 30 (1). pp. 1-4. ISSN 0256-307X 10.1088/0256-307X/30/1/010304 English |
| spellingShingle | Chan, Kar Tim Zainuddin, Hishamuddin Molladavoudi, Saeid Computation of quantum bound states on a singly punctured two-torus |
| title | Computation of quantum bound states on a singly punctured two-torus |
| title_full | Computation of quantum bound states on a singly punctured two-torus |
| title_fullStr | Computation of quantum bound states on a singly punctured two-torus |
| title_full_unstemmed | Computation of quantum bound states on a singly punctured two-torus |
| title_short | Computation of quantum bound states on a singly punctured two-torus |
| title_sort | computation of quantum bound states on a singly punctured two-torus |
| url | http://psasir.upm.edu.my/id/eprint/30081/ http://psasir.upm.edu.my/id/eprint/30081/ http://psasir.upm.edu.my/id/eprint/30081/1/Computation%20of%20quantum%20bound%20states%20on%20a%20singly%20punctured%20two.pdf |