A Probabilistic Method of Characterizing Transit Times for Quantum Particles in Non-Stationary States


We present a probabilistic approach to characterizing the transit time for a quantum particle to flow between two spatially localized states. The time dependence is investigated by initializing the particle in one spatially localized “orbital” and following the time development of the corresponding non-stationary wavefunction of the time-independent Hamiltonian as the particle travels to a second orbital. We show how to calculate the probability that the particle, initially localized in one orbital, has reached a second orbital after a given elapsed time. To do so, discrete evaluations of the time-dependence of orbital occupancy, taken using a fixed time increment, are subjected to conditional probability analysis with the additional restriction of minimum flow rate. This approach yields transit-time probabilities that converge as the time increment used is decreased. The method is demonstrated on cases of two-state oscillations and shown to produce physically realistic results.

Share and Cite:

H. Kim and K. Sohlberg, "A Probabilistic Method of Characterizing Transit Times for Quantum Particles in Non-Stationary States," Journal of Modern Physics, Vol. 4 No. 8, 2013, pp. 1080-1090. doi: 10.4236/jmp.2013.48145.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] R. Baer and D. Neuhauser, Chemical Physics, Vol. 281, 2002, pp. 353-362. doi:10.1016/S0301-0104(02)00570-0
[2] A. B. Pacheco and S. S. Iyengar, Journal of Chemical Physics, Vol. 133, 2010, Article ID: 044105. doi:10.1063/1.3463798
[3] H. Guo, L. Liu and K.-Q. Lao, Chemical Physics Letters, Vol. 218, 1994, pp. 212-220. doi:10.1016/0009-2614(93)E1473-T
[4] C. Joachim, Proceedings of the National Academy of Sciences, Vol. 102, 2005, pp. 8801-8808. doi:10.1073/pnas.0500075102
[5] A. Nitzan, J. Jortner, J. Wilkie, A. L. Burin and M. A. Ratner, The Journal of Physical Chemistry B, Vol. 104 2000, pp. 5661-5665. doi:10.1021/jp0007235
[6] W. R. Cook, R. D. Coalson and D. G. Evans, The Journal of Physical Chemistry B, Vol. 113, 2009, pp. 11437-11447. doi:10.1021/jp9007976
[7] J.-P. Launay, Chemical Society Reviews, Vol. 30, 2001, pp. 386-397. doi:10.1039/b101377g
[8] J. A. Hauge and E. H. Støvneng, Reviews of Modern Physics, Vol. 61, 1989, pp. 917-936. doi:10.1103/RevModPhys.61.917
[9] H. G. Winful, Physics Reports, Vol. 436, 2006, pp. 1-69. doi:10.1016/j.physrep.2006.09.002
[10] Y. Aharonov, N. Erez and B. Reznik, Physical Review A, Vol. 65, 2002, Article ID: 052124. doi:10.1103/PhysRevA.65.052124
[11] J. M. Deutch and F. E. Low, Annals of Physics, Vol. 228, 1993, pp. 184-202. doi:10.1006/aphy.1993.1092
[12] F. E. Low and P. F. Mende, Annals of Physics, Vol. 210, 1991, pp. 380-387. doi:10.1016/0003-4916(91)90047-C
[13] R. S. Dumont and T. L. Marchioro II, Physical Review A, Vol. 47, 1993, pp. 85-97. doi:10.1103/PhysRevA.47.85
[14] L. M. Baskin and D. G. Sokolovskii, Russian Physics Journal, Vol. 30, 1987, pp. 204-206.
[15] P. Pfeifer, Physical Review Letters, Vol. 70, 1993, pp. 3365-3368. doi:10.1103/PhysRevLett.70.3365
[16] R. J. Gordon and S. A. Rice, Annual Review of Physical Chemistry, Vol. 48, 1997, pp. 601-641. doi:10.1146/annurev.physchem.48.1.601
[17] D. Bohm, “Quantum Theory,” Prentice Hall, Englewood Cliffs, 1951.
[18] Mathworks, MATLAB, 1984-2010.
[19] H. F. Hameka and J. R. de la Vega, Journal of the American Chemical Society, Vol. 106, 1984, pp. 7703-7705 doi:10.1021/ja00337a009

Copyright © 2021 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.