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We present a probabilistic approach to characterizing the transittime for a quantum particle to flow between two spatially localized states. Thetime dependence is investigated by initializing the particle in one spatiallylocalized -orbital- and following the time development of the correspondingnon-stationary wavefunction of the time-independent Hamiltonian as the particletravels to a second orbital. We show how to calculate the probability that theparticle, initially localized in one orbital, has reached a second orbitalafter a given elapsed time. To do so, discrete evaluations of thetime-dependence of orbital occupancy, taken using a fixed time increment, aresubjected to conditional probability analysis with the additional restrictionof minimum flow rate. This approach yields transit-time probabilities that convergeas the time increment used is decreased. The method is demonstrated on cases oftwo-state oscillations and shown to produce physically realistic results.

KEYWORDS

Conditional Probability; Non-Stationary Quantum Particle; Transit Time

Cite this paper

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.





Author: Hae-Won Kim, Karl Sohlberg

Source: http://www.scirp.org/



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