1. Maass Cusp Forms on Singly Punctured Two-Torus
- Author
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Abubaker Ahmed Mohamed Siddig, Nurisya Mohd Shah, Hishamuddin Zainuddin, Swee-Ping Chia, Kurunathan Ratnavelu, and Muhamad Rasat Muhamad
- Subjects
Cusp (singularity) ,Pure mathematics ,Mathematics::Number Theory ,Mathematical analysis ,Torus ,Mathematics::Geometric Topology ,Quantum chaos ,symbols.namesake ,Special functions ,Bound state ,symbols ,Quantum ,Bessel function ,Eigenvalues and eigenvectors ,Mathematics - Abstract
Quantum mechanical systems on punctured surfaces modeled by hyperbolic spaces can play an interesting role in exploring quantum chaos and in studying behaviour of future quantum nano‐devices. The case of singly‐punctured two‐torus, for example, has been well‐studied in the literature particularly for its scattering states. However, the bound states on the punctured torus given by Maass cusp forms are lesser known. In this note, we report on the algorithm of numerically computing these functions and we present ten lower‐lying eigenvalues for each odd and even Maass cusp forms.
- Published
- 2009
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