Integrating the quantum Hamilton-Jacobi equations by wavefront expansion and phase space analysis

Journal of Chemical Physics

Volumn 113, Issue 20, 2000, Pages 8888-8897

  Bittner, Eric R ^a   Wyatt, Robert E ^b  

^a University of Houston   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; CONVERGENCE OF NUMERICAL METHODS; EQUATIONS OF MOTION; HYDRODYNAMICS; INTEGRATION; LEAST SQUARES APPROXIMATIONS; PHASE SPACE METHODS;

QUANTUM HAMILTON-JACOBI EQUATIONS;

QUANTUM THEORY;

EID: 0034318880     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1319987     Document Type: Article

References (27)

1. C. L. Lopreore and R. E. Wyatt, Phys. Rev. Lett. 82, 5190 (1999).
2. R. E. Wyatt, Chem. Phys. Lett. 313, 189 (1999).
3. R. E. Wyatt, J. Chem. Phys. 111, 4406 (1999).
4. J. C. Burant and J. C. Tully, J. Chem. Phys. 112, 6097 (2000).
5. E. R. Bittner, J. Chem. Phys. 112, 9703 (2000).
6. B. K. Day, A. Askar, and H. A. Rabitz, J. Chem. Phys. 109, 8770 (1998).
7. F. S. Mayor, A. Askar, and H. A. Rabitz, J. Chem. Phys. 111, 2423 (1999).
8. L. de Broglie, C. R. Acad. Sci. Paris 183, 447 (1926).
9. E. Madelung, Z. Phys. 40, 322 (1926).
10. D. Bohm, Phys. Rev. 85, 166 (1952).
11. D. Bohm, Phys. Rev. 84, 180 (1952).
12. R. E. Wyatt and E. R. Bittner, J. Chem. Phys. 113, 8898 (2000), following paper.
13. D. Bohm and B. Hiley, The Undivided Universe (Cambridge University Press, Cambridge, 1993).
14. P. R. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993).
15. P. R. Holland, Phys. Rep. 224, 95 (1993).
16. S. Goldstein, Phys. Today 51, 42 (1998).
17. S. Goldstein, Phys. Today 51, 38 (1998).
18. O. F. de Alcantara-Bonfin, J. Florencio, and F. C. Sa Barreto, Phys. Rev. E 58, 6851 (1998).
19. N. Pinto-Neto and E. Santini, Phys. Rev. D 59, 123517 (1999).
20. V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, Berlin, 1978).
21. See, for example, W. H. Press, B. P. Flannery, S. Teukolsky, and W. T. Vettering, Numerical Recipies (Cambridge University Press, Cambridge, 1986).
22. R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985).
23. J. M. Thijssen, Computational Physics (Cambridge University Press, Cambridge, 1999).
24. R. Glowinski, University of Houston (private communication, 2000).
25. J. I. Steinfeld, J. S. Francisco, and W. L. Hase, Chemical Kinetics and Dynamics (Prentice-Hall, Englewood Cliffs, 1989).
26. A. I. Ioselevich and E. Rashba, in Quantum Tunneling in Condensed Media, edited by V. M. Agranovich and A. A. Maradudin (Elsevier, Amsterdam, 1992).
27. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).