Computing Quantum Bound States on Triply Punctured Two-Sphere Surface

Journal Article
Siddig, K. T. Chan, H. Zainuddin, K. A. M. Atan, A. A. . 2016
Publication Work Type: 
Research
Magazine \ Newspaper: 
CHIN. PHYS. LETT
Issue Number: 
9
Volume Number: 
33
Pages: 
4
Publication 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.