Computation of Quantum Bound States on a Singly Punctured Two-Torus

doi:10.1088/0256-307X/30/1/010304

Chin. Phys. Lett.

2013, Vol. 30

Issue (1): 010304 DOI: 10.1088/0256-307X/30/1/010304

GENERAL

Computation of Quantum Bound States on a Singly Punctured Two-Torus

CHAN Kar-Tim^1*, Hishamuddin Zainuddin^1,2, Saeid Molladavoudi²

¹Department of Physics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
²Laboratory of Computational Sciences and Mathematical Physics, Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

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CHAN Kar-Tim, Hishamuddin Zainuddin, Saeid Molladavoudi 2013 Chin. Phys. Lett. 30 010304

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Abstract 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.

Received: 11 October 2012 Published: 04 March 2013

PACS:	03.65.Ge	(Solutions of wave equations: bound states)
	02.40.-k	(Geometry, differential geometry, and topology)

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https://cpl.iphy.ac.cn/10.1088/0256-307X/30/1/010304 OR https://cpl.iphy.ac.cn/Y2013/V30/I1/010304

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	CHAN Kar-Tim
	Hishamuddin Zainuddin
	Saeid Molladavoudi

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