We have solved the problem of determining the traversal time distribution for a quantum transition between arbitrary initial and final states. This distribution is given by a Fourier transform of the Feynman averaged characteristic function for the classical traversal time functional ${\mathit{t}}_{\mathrm{ab}}^{\mathrm{cl}}$ [x(t)]. For one-dimensional tunneling, the distributions for the dwell, reflection, and transmission times are determined for an arbitrary potential V(x). All three distributions are complex valued and require the concept of negative probability.We have solved the problem of determining the traversal time distribution for a quantum transition between arbitrary initial and final states. This distribution is given by a Fourier transform of the Feynman averaged characteristic function for the classical traversal time functional ${\mathit{t}}_{\mathrm{ab}}^{\mathrm{cl}}$[x(t)]. For one-dimensional tunneling, the distributions for the dwell, reflection, and transmission times are determined for an arbitrary potential V(x). All three distributions are complex valued and require the concept of negative probability.

Physical Review AAug 1, 199162 citations

Traversal time for quantum tunneling

Ming‐Quey Chen, M.S. Wang

Physics Letters AOct 1, 199021 citations

Traversal Time in Tunneling

Rolf W. Landauer

Abstract Traversal time in tunneling has become a somewhat controversial subject, and this note presents a personal perspective on some of these discussions. There is a widely invoked linear relationship yielding dwell time as a weighted average of traversal time and reflection time. I assert that it is totally without basis. Many authors follow wave packets through barriers. The results of such calculations are hard to correlate with experiment. Stevens has provided a wave packet approach which avoids some of the problems typically faced by such analyses; nevertheless its analytical details are questioned. The significance of complex traversal times, favored by some investigators, is questioned. The relative merit of various possible “clocks” in the analysis of traversal time is discussed, but without definitive conclusions.Abstract Traversal time in tunneling has become a somewhat controversial subject, and this note presents a personal perspective on some of these discussions. There is a widely invoked linear relationship yielding dwell time as a weighted average of traversal time and reflection time. I assert that it is totally without basis. Many authors follow wave packets through barriers. The results of such calculations are hard to correlate with experiment. Stevens has provided a wave packet approach which avoids some of the problems typically faced by such analyses; nevertheless its analytical details are questioned. The significance of complex traversal times, favored by some investigators, is questioned. The relative merit of various possible “clocks” in the analysis of traversal time is discussed, but without definitive conclusions.

Berichte der Bunsengesellschaft für physikalische ChemieMar 1, 199165 citations

Trajectories and Traversal Times in Quantum Tunneling

Zhi Hong Huang

Jan 1, 19890 citations

{\mathit{t}}_{\mathrm{ab}}^{\mathrm{cl}}

[x(t)]. For one-dimensional tunneling, the distributions for the dwell, reflection, and transmission times are determined for an arbitrary potential V(x). All three distributions are complex valued and require the concept of negative probability.