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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Bibliographic Details
Published in:Chinese physics letters 2016-09, Vol.33 (9), p.1-4
Main Authors: Chan, K. T., Zainuddin, H., Atan, K. A. M., Siddig, A. A.
Format: Article
Language:English
Subjects:
双曲度量
平方可积函数
球面
离散特征值
表面特征
计算结果
量子力学系统
量子束缚态
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Summary: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.
ISSN:0256-307X
1741-3540
DOI:10.1088/0256-307X/33/9/090301