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.