Research Article
Year 2020,
, 539 - 552, 02.04.2020
Abstract
References
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- [10] T. Tang, The Hermite spectral method for Gaussian-type functions, SIAM J. Sci. Comput. 14 (3), 594–606, 1993.
- [11] H. Taşeli, Modified Laguerre basis for hydrogen-like systems, Int. J. Quantum Chem. 63, 949–959, 1997.
- [12] H. Taşeli and H. Alıcı, The Laguerre pseudospectral method for the reflection sym- metric Hamiltonians on the real line, J. Math. Chem. 41, 407–416, 2007.
- [13] H. Taşeli and R. Eid, Eigenvalues of the two-dimensional Schrödinger equation with nonseparable potentials, Int. J. Quantum Chem. 59, 183–201, 1996.
- [14] J.A.C. Weideman and L.N. Trefethen, Eigenvalues of second-order spectral differen- tiation matrices, SIAM J. Numer. Anal. 25, 1279–1298, 1988.
The Laguerre pseudospectral method for the two-dimensional Schrödinger equation with symmetric nonseparable potentials
Abstract
The Hermite pseudospectral method is one of the natural techniques for the numerical treatment of the problems defined over unbounded domains such as two-dimensional time-independent Schrödinger equation on the whole real plane. However, it is shown here that for the symmetric potentials, transformation of the problem over the first quadrant and the application of the Laguerre pseudospectral method reduce the cost by a factor of four when compared to the Hermite pseudospectral method.
Keywords
The Laguerre pseudospectral method two dimensional Schrödinger equation symmetric potentials
References
- [1] H. Alıcı, The Hermite pseudospectral method for the two-dimensional Schrödinger equation with nonseparable potentials, Comput. Math. Appl. 69 (6), 466–477, 2015.
- [2] H. Alıcı and H. Taşeli, Pseudospectral methods for an equation of hypergeometric type with a perturbation, J. Comput. Appl. Math. 234, 1140–1152, 2010.
- [3] M. Demiralp, N.A. Baykara, and H. Taşeli, A basis set comparison in a variational scheme for Yukawa potential, J. Math. Chem. 11, 311–323, 1992.
- [4] G.H. Golub and J.H. Welsch, Calculation of Gauss quadrature rules, Math. Comput. 23, 221–230 s1–s10, 1969.
- [5] B.-Y. Guo, L.-L. Wang, and Z.-Q. Wang, Generalized Laguerre interpolation and pseudospectral method for unbounded domains, SIAM J. Numer. Anal. 43, 2567–2589, 2006.
- [6] F.B. Hildebrand, Method of Applied Mathematics, McGraw-Hill, NewYork, 1956, pp. 319–323.
- [7] G. Mastroianni and D. Occorsio, Lagrange interpolation at Laguerre zeros in some weighted uniform spaces, Acta Math. Hungar. 91 (1-2), 27–52, 2001.
- [8] J. Shen, Stable and efficient spectral methods in unbounded domains using Laguerre functions, SIAM J. Numer. Anal. 38 (4), 1113–1133, 2000.
- [9] J. Shen and L.-L. Wang, Some recent advances on spectral methods for unbounded domains, Commun. Comput. Phys. 5, 195–241, 2009.
- [10] T. Tang, The Hermite spectral method for Gaussian-type functions, SIAM J. Sci. Comput. 14 (3), 594–606, 1993.
- [11] H. Taşeli, Modified Laguerre basis for hydrogen-like systems, Int. J. Quantum Chem. 63, 949–959, 1997.
- [12] H. Taşeli and H. Alıcı, The Laguerre pseudospectral method for the reflection sym- metric Hamiltonians on the real line, J. Math. Chem. 41, 407–416, 2007.
- [13] H. Taşeli and R. Eid, Eigenvalues of the two-dimensional Schrödinger equation with nonseparable potentials, Int. J. Quantum Chem. 59, 183–201, 1996.
- [14] J.A.C. Weideman and L.N. Trefethen, Eigenvalues of second-order spectral differen- tiation matrices, SIAM J. Numer. Anal. 25, 1279–1298, 1988.
There are 14 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | April 2, 2020 |
| Published in Issue | Year 2020 |