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J. A. Hauge and E. H. Støvneng, Reviews of Modern Physics, Vol. 61, 1989, pp. 917-936. doi:10.1103/RevModPhys.61.917

has been cited by the following article:

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

    AUTHORS: Hae-Won Kim, Karl Sohlberg

    KEYWORDS: Conditional Probability; Non-Stationary Quantum Particle; Transit Time

    JOURNAL NAME: Journal of Modern Physics, Vol.4 No.8, August 13, 2013

    ABSTRACT: 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.