Skip to main content

Applications of the Quantum Trajectory Method

  • Chapter
Quantum Dynamics with Trajectories

Part of the book series: Interdisciplinary Applied Mathematics ((IAM,volume 28))

  • 2143 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.00
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Lopreore and R.E. Wyatt, Quantum wave packet dynamics with trajectories, Phys. Rev. Lett. 82, 5190 (1999).

    Article  Google Scholar 

  2. R.E. Wyatt, Quantum wave-packet dynamics with trajectories: wave function synthesis along quantum paths, Chem. Phys. Lett. 313, 189 (1999).

    Article  Google Scholar 

  3. R.E. Wyatt, Quantum wave packet dynamics with trajectories: Application to reactive scattering, J. Chem. Phys. 111, 4406 (1999).

    Article  Google Scholar 

  4. E.R. Bittner and R.E. Wyatt, Integrating the quantum Hamilton-Jacobi equations by wave-front expansion and phase space analysis, J. Chem. Phys. 113, 8888 (2000).

    Article  Google Scholar 

  5. R.E. Wyatt and E.R. Bittner, Quantum wave packet dynamics with trajectories: Implementation with adaptive Lagrangian grids, J. Chem. Phys. 113, 8898 (2000).

    Article  Google Scholar 

  6. C. Lopreore and R.E. Wyatt, Quantum wave packet dynamics with trajectories: reflections on a downhill ramp potential, Chem. Phys. Lett. 325, 73 (2000).

    Article  Google Scholar 

  7. E.R. Bittner, Quantum tunneling dynamics using hydrodynamic trajectories, J. Chem. Phys. 112, 9703 (2000).

    Article  Google Scholar 

  8. R.E. Wyatt, D.J. Kouri, and D.K. Hoffman, Quantum wave packet dynamics with trajectories: Implementation with distributed approximating functionals, J. Chem. Phys. 112, 10730 (2000).

    Article  Google Scholar 

  9. R.E. Wyatt and K. Na, Quantum trajectory analysis of multimode subsystem-bath dynamics, Phys. Rev. E. 65, 016702 (2001).

    Article  Google Scholar 

  10. C. Lopreore, R.E. Wyatt, and G. Parlant, Electronic transitions with quantum trajectories, J. Chem. Phys. 114, 5113 (2001).

    Article  Google Scholar 

  11. C. Lopreore and R.E. Wyatt, Electronic transitions with quantum trajectories. II, J. Chem. Phys. 116, 1228 (2001).

    Article  Google Scholar 

  12. K. Na and R.E. Wyatt, Quantum hydrodynamic analysis of decoherence: quantum trajectories and stress tensor, Phys. Lett. A 306, 97 (2002).

    Article  Google Scholar 

  13. C. Trahan and R.E. Wyatt, Radial basis function interpolation in the quantum trajectory method: optimization of the mutiquadric shape parameter, J. Comp. Phys. 185, 27 (2003).

    Article  Google Scholar 

  14. D. Nerukh and J.H. Frederick, Multidimensional quantum dynamics with trajectories: a novel numerical implementation of Bohmian mechanics, Chem. Phys. Lett. 332, 145 (2000).

    Article  Google Scholar 

  15. R.K. Vadapalli, C.A. Weatherford, I. Banicescu, R.L. Carino, and J. Zhu, Transient effect of a free particle wave packet in the hydrodynamic formulation of the time-dependent Schrödinger equation, Int. J. Quantum Chem. 94, 1 (2003).

    Article  Google Scholar 

  16. X. Hu, T. Ho, H. Rabitz, and A. Askar, Solution of the quantum fluid dynamical equations with radial basis function interpolation, Phys. Rev. E 61, 5967 (2000).

    Article  Google Scholar 

  17. F. Sales Mayor, A. Askar, and H.A. Rabitz, Quantum fluid dynamics in the Lagrangian representation and applications to photodissociation problems, J. Chem. Phys. 111, 2423 (1999).

    Article  Google Scholar 

  18. P. R. Holland, The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics (Cambridge University Press, New York, 1993).

    Google Scholar 

  19. W. Haussmann, K. Jetter, and M. Reimer (eds.), Recent progress in multivariate approximation. Proceedings of the 4th International Conference on Multivariate Approximation held at the University of Dortmund (Birkhäuser Verlag, Basel, 2001).

    Google Scholar 

  20. T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Springer, New York, 2001).

    Google Scholar 

  21. S. Rippa, An algorithm for selecting a good value for the parameter c in radial basis function interpolation, Adv. Comp. Math. 11, 193 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  22. N.J.D. Powell, A review of methods for multivariable interpolation at scattered data points: The state of the art in numerical analysis (Oxford University Press, NewYork, 1997).

    Google Scholar 

  23. M.A. Goldberg, C.S. Chen, and S.R. Karur, Improved multiquadric approximation for partial differential equations, Eng. Anal. with Boundary Elements. 18, 9 (1996).

    Article  Google Scholar 

  24. M.A. Goldberg and C.S. Chen, A bibliography on radial basis function approximation, Boundary Elem. Commun. 7, 155 (1996).

    Google Scholar 

  25. R. Schaback, Creating Surfaces From Scattered Data Using Radial Basis Functions. Mathematical Methods for Curves and Surfaces (Vanderbilt Univ. Press, Tennessee, 1995).

    Google Scholar 

  26. E.J. Kansa and R.E. Carlson, Improved accuracy of multiquadric interpolation using variable shape parameters, Comp. Math. Appl. 24, 99 (1992).

    Article  MathSciNet  Google Scholar 

  27. T.A. Foley and R. Carlson, The Parameter R2 in Multiquadric Interpolation, Comp. Math. Appl. 21, 29 (1991).

    MathSciNet  Google Scholar 

  28. R.L. Hardy, Theory and applications of the multiquadric-biharmonic method. Comp. Math. Appl. 19, 163 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  29. E.J. Kansa, Multiquadrics: A scattered data approximation scheme with applications to computational fluid dynamics. I, Comp. Math. Applic. 19, 127 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  30. R. Franke, Scattered data interpolation: A test of some methods, Math. Comp. 38, 157 (1982).

    Article  MathSciNet  Google Scholar 

  31. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in FORTRAN 90, (Cambridge, University Press, 1996).

    Google Scholar 

  32. yepes.rice.edu/PhysicsApplets/

    Google Scholar 

  33. G.E. Bowman, Bohmian mechanics as a heuristic device: Wave packets in the harmonic oscillator, Am. J. Phys. 70, 313 (2002).

    Article  Google Scholar 

  34. www.cm.utexas.edu/Wyatt/movies/qtm

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer Science+Business Media, Inc.

About this chapter

Cite this chapter

Trahan, C.J. (2005). Applications of the Quantum Trajectory Method. In: Quantum Dynamics with Trajectories. Interdisciplinary Applied Mathematics, vol 28. Springer, New York, NY. https://doi.org/10.1007/0-387-28145-2_6

Download citation

Publish with us

Policies and ethics