Numerical method for computing Maass cusp forms on triply punctured two-sphere
- Department of Physics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor (Malaysia)
- Department of Physics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor (Malaysia)
A quantum mechanical system on a punctured surface modeled on hyperbolic space has always been an important subject of research in mathematics and physics. This corresponding quantum system is governed by the Schrödinger equation whose solutions are the Maass waveforms. Spectral studies on these Maass waveforms are known to contain both continuous and discrete eigenvalues. The discrete eigenfunctions are usually called the Maass Cusp Forms (MCF) where their discrete eigenvalues are not known analytically. We introduce a numerical method based on Hejhal and Then algorithm using GridMathematica for computing MCF on a punctured surface with three cusps namely the triply punctured two-sphere. We also report on a pullback algorithm for the punctured surface and a point locater algorithm to facilitate the complete pullback which are essential parts of the main algorithm.
- OSTI ID:
- 22266013
- Journal Information:
- AIP Conference Proceedings, Vol. 1588, Issue 1; Conference: 4. international meeting on frontiers in physics, Kuala Lumpur (Malaysia), 27-30 Aug 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
Similar Records
On relations between analytic modular forms and Maass waveforms for PSL(2,Z)
Supersymmetric quantum cosmological billiards