Solving the bound-state Schrödinger equation by reproducing kernel interpolation

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 2, 2000, Pages 2074-2085

  Hu, Xu Guang ^a   Ho, Tak San ^a   Rabitz, Herschel ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BINDING ENERGY; MATHEMATICAL OPERATORS; MORSE POTENTIAL; RADIAL BASIS FUNCTION NETWORKS;

ASYMPTOTIC SOLUTIONS; DISSOCIATION LIMIT; FUNCTIONAL METHODS; LINEAR OPERATORS; RADIAL BASIS FUNCTIONS; REPRODUCING KERNEL; REPRODUCING KERNEL HILBERT SPACES; REPRODUCING KERNEL INTERPOLATIONS;

NUMERICAL METHODS;

EID: 0000216398     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.2074     Document Type: Article

References (39)

1. Numerical Grid Methods and Their Applications to Schödinger Equation, edited by C. Cerjan (Kluwer Academic, Dordrecht 1993).
2. J. C. Light, I. P. Hamilton, and J. V. Lill, J. Chem. Phys. 82, 1400 (1985).
3. D. Baye and P. H. Heenen, J. Phys. A 19, 2041 (1986).
4. J. T. Muckerman, Chem. Phys. Lett. 173, 200 (1990).
5. D. T. Colbert and W. H. Miller, J. Chem. Phys. 96, 1982 (1992).
6. B. S. Shizgal and H. Chen, J. Chem. Phys. 104, 4137 (1996).
7. B. I. Schneider, Phys. Rev. A 55, 3417 (1997).
8. H. Karabulut and E. L. Silbert III, J. Phys. A 30, L513 (1997).
9. D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, 3rd. Printing (SIAM, Philadelphiia, 1983).
10. R. Kosloff, in Dynamics of Molecules and Chemical Reactions, edited by R. E. Wyatt and J. Z. H. Zhang (Marcel Dekker, New York, 1996).
11. B. W. Shore, J. Chem. Phys. 59, 6450 (1973).
12. M. J. Davis and E. J. Heller, J. Chem. Phys. 71, 3383 (1979).
13. I. P. Hamilton and J. C. Light, J. Chem. Phys. 84, 306 (1986).
14. W. Yang and A. C. Peet, Chem. Phys. Lett. 153, 98 (1988).
15. Z. Bačić and J. C. Light, Annu. Rev. Phys. Chem. 40, 469 (1989).
16. G. W. Wei, D. S. Zhang, D. J. Kouri, and D. K. Hoffman, Phys. Rev. Lett. 79, 775 (1997).
17. D. K. Hoffman, G. W. Wei, D. S. Zhang, and D. J. Kouri, Phys. Rev. E 57, 6152 (1997), and references therein.
18. D. S. Zhang, G. W. Wei, D. J. Kouri, and D. K. Hoffman, J. Chem. Phys. 106, 5216 (1996).
19. D. K. Hoffman, T. L. Marchioro II, M. Arnold, Y. Huang, W. Zhu, and D. J. Kouri, J. Math. Chem. 20, 117 (1994).
20. T.-S. Ho and H. Rabitz, J. Chem. Phys. 104, 2584 (1995)
21. J. Chem. Phys.T.-S. HoH. Rabitz105, 10 472 (1996).
22. T. Hollebeek, T.-S. Ho, and H. Rabitz, J. Chem. Phys. 106, 7223 (1997).
23. G. C. Schatz, A. Papaionnou, L. A. Pederson, L. R. Harding, T. Ho Hebeek, T.-S. Ho, and H. Rabitz, J. Chem. Phys. 107, 2340 (1997).
24. H.-G. Hu, T.-S. Ho, and H. Rabitz, Chem. Phys. Lett. 288, 719 (1998).
25. C. de Boor and R. E. Lynch, J. Math. Mech. 15, 953 (1966).
26. G. Wahba, Spline Models for Observational Data (SIAM, Philadelphia, 1990).
27. N. Aronszajn, Trans. Am. Math. Soc. 68, 337 (1950).
28. R. Schaback, in Vol. 1 of Approximation and Interpolation, Approximation Theory VII, edited by C. K. Chui and L. L. Schumaker (World Scientific, Singapore, 1995), p. 491.
29. N. J. D. Powell, in Advances in numerical Analysis II: Wavelets, Subdivision Algorithms, and Radial Basis Functions, edited by W. A. Light (Oxford University Press, Oxford, 1992), p. 105.
30. M. H. Kalos, Phys. Rev. 128, 1791 (1962)
31. S. Zhang and M. H. Kalos, Phys. Rev. Lett. 67, 3074 (1991).
32. D. R. Adams and L. I. Hedberg, Function Spaces and Potential Theory (Springer-Verlag, Berlin, 1996).
33. A. Aronszajn and K. T. Smith, Ann. Inst. Fourier 11, 385 (1961).
34. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980).
35. R. Schaback, Ann. Numer. Math. 4, 537 (1997).
36. R. Schaback, in Multivariate Approximations: From CAGD to Wavelets, edited by K. Jetter and F. Utreras (World Scientific, Singpore, 1993), p. 293.
37. X.-G. Hu, T.-S. Ho, and H. Rabitz, Comput. Phys. Commun. 113, 168 (1998).
38. R. Franke, Math. Comput. 38, 181 (1982).
39. H. Wei, J. Chem. Phys. 106, 6885 (1997).