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The electronic states of halide ions are modeled by a one-dimensional Ž . y x 2 Hamiltonian with a potential V x s yV e . The two parameters V and are fixed 0 0 0

ABSTRACT:We suggest a recipe for calculating the time taken by a particle to tunnel out from an initially localized state in one of the wells of symmetrical doublewell potential into the other well. We calculate average velocity ͗v ͘ of the tunneling particle by solving the Schrö dinger equation numerically for ⌿(x, t), then estimating ͗v(t)͘ ϭ (d/dt)͗x(t)͘ and time-averaging it. The time taken to tunnel is measured by calculating av ϭ l 0 /͗v ͘ where l 0 is an idealized estimate of the barrier width. We suggest an approximate partitioning of av into an intrinsic decay time ( d ) and a barrier crossing time ( b ), d being obtained from energy spread of the packet. av Ϫ d is shown to be close to the Wentzel-Brillouin-Kramers estimate of barrier crossing time sc . The response of av to an external driving field and nonzero temperatures are tested. We also apply the method to a purely barrier penetration problem as well as to the problem of tunneling through a fluctuating barrier.

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