The eigenenergies of the wave function through the non-variational Galerkin-B-spline approach

Applied Mathematics and Computation

Volumn 178, Issue 2, 2006, Pages 486-492

  Nine, B ^a   Haif Khaif, O ^a   Zerarka, A ^a  

^a UNIVERSITY OF BISKRA   (Algeria)

Author keywords

B spline; Eigenenergies; Galerkin; Variational; Wave function

Indexed keywords

GALERKIN METHODS; HAMILTONIANS; MATRIX ALGEBRA; NONLINEAR EQUATIONS; WAVE EQUATIONS;

B-SPLINE; EIGENENERGIES; GALERKIN-B-SPLINE; ROTATION BOUND STATES; VARIATIONAL; WAVE FUNCTIONS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 33746208838     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.11.067     Document Type: Article

References (26)

1. Fischer C., and Idrees M. Spline methods for resonances in photoionization cross sections. J. Phys. B 23 (1990) 679
2. Morrison J.C., and Bottcher C. Spline collocation methods for calculating orbital energies. J. Phys. B: At. Mol. Opt. Phys. 26 (1993)
3. Johnson W.R., Blundell S.A., and Sapirstein J. Finite basis sets for the Dirac equation constructed from B splines. Phys. Rev. A 37 (1988)
4. Sinha A., Roychoudhury R., and Varshni Y.P. Shifted 1/N expansion for confined quantum systems. Can. J. Phys. 78 (2000) 141
5. Zerarka A., Hassouni S., Saidi H., and Boumedjane Y. Energy spectra of the Schrödinger equation and the differential quadrature method. Commun. Nonlinear Sci. Numer. Simul. 10 (2005)
6. Selg M. Numerically complemented analytic method for solving the time-independent one-dimensional Schrödinger equation. Phys. Rev. E 64 5 (2001) 056701
7. -1/3. IL Nuovo Cimento B 109 (1994) 1217
8. Bose S.K., and Gupta N. Exact solution of nonrelativistic Schrödinger equation for certain central physical potentials. IL Nuovo Cimento B 113 (1998) 299
9. Braun M., Sofianos S.A., Papageorgiou D.G., and Lagaris I.E. An efficient Chebyshev-Lanczos method for obtaining eigensolutions of the Schrödinger equation on a grid. J. Comput. Phys. 126 (1996) 315
10. Dong S.H. Exact solutions of the two-dimensional Schrödinger equation with certain central potentials. Int. J. Theor. Phys. 39 (2000) 1119
11. Iachello F. Algebraic methods in quantum mechanics with applications to nuclear and molecular structure. Nucl. Phys. A 560 (1993) 23-34
12. Varshni Y.P. Eigenstates and oscillator strengths for the Hulthén potential. Phys. Rev. A 41 (1990) 4682
13. Landtman M., Laughlin C., Shen Y.T., and Hansen J.E. The introduction of orthogonality constraints in basis set calculations. J. Phys. B 26 (1993) 1080
14. Fang T.K., and Chang T.N. B-spline-based multichannel K-matrix method for atomic photoionization. Phys. Rev. A 61 (2000)
15. van der Hart H. B-spline methods in R-matrix theory for scattering in two-electron systems. J. Phys. B 30 (1997)
16. Prenter P.M. Splines and Variational Methods (1975), Wiley-Interscience, New York
17. Dierckx P. Curve and Surface Fitting with Splines (1993), Clarenton Press, Oxford
18. de Boor C. A Practical Guide to Splines (1978), Springer, New York
19. Garbow B.S., Boyle J.M., Dongarra J.J., and Moler C.B. Matrix Eigensystem Routines-Eispack guide Extension (1977), Springer, Berlin
20. Umar A.S., Wu J., Strayer M.R., and Bottcher C. The basis-spline collocation method for the lattice solution of boundary value problems. J. Comput. Phys. 93 (1991) 426
21. Brage T., Fischer C.F., and Miecznik G. Non-variational, spline-Galerkin calculations of resonance positions and widths, and photodetachment and photoionization cross sections for H and He. J. Phys. B 25 (1992) 5289
22. Atluri S.N., and Shen S. The Meshless Local Petrov-Galerkin (MLPG) Method (2002), Tech Science Press, Encino, CA
23. Atluri S.N., and Shen S. The meshless local Petrov-Galerkin (MLPG) method: a simple & less costly alternative to the finite element and boundary element methods. Comput. Modell. Eng. Sci. 3 1 (2002) 11-51
24. Morse P.M. Diatomic molecules according to the wave mechanics. II. Vibrational levels. Phys. Rev. 34 (1929) 57
25. Morales D.A. Energy eigenstates of the rotating Morse oscillator using the shifted 1/N expansion. Chem. Phys. Lett. 161 (1989) 253
26. Bag M., Panja M.M., Dutt R., and Varshni Y.P. Modified shifted large-N approach to the Morse oscillator. Phys. Rev. A 46 (1992) 6059