Computing Quantum Bound States on Triply Punctured Two-Sphere Surface
K. T. Chan1,2**, H. Zainuddin1,2, 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
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.
. [J]. 中国物理快报, 2016, 33(09): 90301-090301.
K. T. Chan, H. Zainuddin, K. A. M. Atan, A. A. Siddig. Computing Quantum Bound States on Triply Punctured Two-Sphere Surface. Chin. Phys. Lett., 2016, 33(09): 90301-090301.
2016, Vol. 33 
