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Computing quantum bound states on triply punctured two-sphere surface


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


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.

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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.1088/0256-307X/33/9/090301
Publisher: Institute of Physics Publishing
Keywords: Quantum mechanical system; Maass cusp forms; Computing quantum bound
Depositing User: Mohd Hafiz Che Mahasan
Date Deposited: 06 Nov 2017 13:24
Last Modified: 06 Nov 2017 13:24
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1088/0256-307X/33/9/090301
URI: http://psasir.upm.edu.my/id/eprint/55354
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