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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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Main Authors: Chan, Kar Tim, Zainuddin, Hishamuddin, Molladavoudi, Saeid
Format: Article
Language:English
English
Published: Institute of Physics 2013
Online Access:http://psasir.upm.edu.my/id/eprint/30081/1/Computation%20of%20quantum%20bound%20states%20on%20a%20singly%20punctured%20two.pdf
http://psasir.upm.edu.my/id/eprint/30081/
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spelling my.upm.eprints.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
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
English
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.
format Article
author Chan, Kar Tim
Zainuddin, Hishamuddin
Molladavoudi, Saeid
spellingShingle Chan, Kar Tim
Zainuddin, Hishamuddin
Molladavoudi, Saeid
Computation of quantum bound states on a singly punctured two-torus
author_facet Chan, Kar Tim
Zainuddin, Hishamuddin
Molladavoudi, Saeid
author_sort Chan, Kar Tim
title 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_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_sort computation of quantum bound states on a singly punctured two-torus
publisher Institute of Physics
publishDate 2013
url http://psasir.upm.edu.my/id/eprint/30081/1/Computation%20of%20quantum%20bound%20states%20on%20a%20singly%20punctured%20two.pdf
http://psasir.upm.edu.my/id/eprint/30081/
_version_ 1643829951998197760
score 13.211869

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