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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Bibliographic Details
Published inChinese physics letters Vol. 30; no. 1; pp. 10304 - 1-010304-4
Main Authors Kar-Tim, Chan, Zainuddin, Hishamuddin, Molladavoudi, Saeid
Format Journal Article
LanguageEnglish
Published 01.01.2013
Subjects
Algorithms
Computation
Eigenfunctions
Eigenvalues
Mathematical analysis
Operators
Quantum mechanics
Waveforms
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Summary: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.
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ISSN:0256-307X
1741-3540
DOI:10.1088/0256-307X/30/1/010304