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

Hae-Won Kim, Karl Sohlberg

Department of Chemistry, Drexel University, Philadelphia, PA, USA.
Department of Chemistry, Penn State Abington, Abington, PA, USA.

DOI: 10.4236/jmp.2013.48145                

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.

Keywords

Conditional Probability; Non-Stationary Quantum Particle; Transit Time

Conflicts of Interest

The authors declare no conflicts of interest.

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