Computing Quantum Bound States on Triply Punctured Two-Sphere Surface

doi:10.1088/0256-307X/33/9/090301

Chin. Phys. Lett.

2016, Vol. 33

Issue (09): 090301 DOI: 10.1088/0256-307X/33/9/090301

GENERAL

Computing Quantum Bound States on Triply Punctured Two-Sphere Surface

K. T. Chan^1,2**, H. Zainuddin^1,2, K. A. M. Atan², A. A. Siddig³

¹Department of Physics, Faculty of Science, Universiti Putra Malaysia, UPM Serdang 43400, Malaysia
²Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang 43400, Malaysia
³Department of Physics and Astronomy, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

Cite this article:

K. T. Chan, H. Zainuddin, K. A. M. Atan et al 2016 Chin. Phys. Lett. 33 090301

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Abstract 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.

Received: 17 March 2016 Published: 30 September 2016

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

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https://cpl.iphy.ac.cn/10.1088/0256-307X/33/9/090301 OR https://cpl.iphy.ac.cn/Y2016/V33/I09/090301

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