A generalized wave function is defined for an arbitrary real functional. Properties of the traversal-time wave function are investigated for one-dimensional scattering at a fixed energy. A Heisenberg-type uncertainty relation is derived from the traversal-time wave function. Traversal-time probability distributions for a Larmor clock measurement are studied in detail. The high-resolution limit of a traversal-time measurement is examined. The use of ``fast'' and ``slow'' arguments in a traversal-time analysis is discussed. The systems studied include free motion, resonance, and nonresonance tunneling through a double-\ensuremath{\delta}-function potential, rectangular barrier, absorbing optical potential, and interaction with a slow oscillator.A generalized wave function is defined for an arbitrary real functional. Properties of the traversal-time wave function are investigated for one-dimensional scattering at a fixed energy. A Heisenberg-type uncertainty relation is derived from the traversal-time wave function. Traversal-time probability distributions for a Larmor clock measurement are studied in detail. The high-resolution limit of a traversal-time measurement is examined. The use of ``fast'' and ``slow'' arguments in a traversal-time analysis is discussed. The systems studied include free motion, resonance, and nonresonance tunneling through a double-\ensuremath{\delta}-function potential, rectangular barrier, absorbing optical potential, and interaction with a slow oscillator.

Physical Review AAug 1, 199447 citations

Trajectories and Traversal Times in Quantum Tunneling

Zhi Hong Huang

Jan 1, 19890 citations

Early times in tunneling

Gastón García‐Calderón, Jorge Villavicencio

Exact analytical solutions of the time-dependent Schrödinger equation with the initial condition of an incident cutoff wave are used to investigate the traversal time for tunneling. The probability density starts from a vanishing value along the tunneling and transmitted regions of the potential. At the barrier width it exhibits, at early times, a distribution of traversal times that typically has a peak $τ_p$ and a width $Δτ$ . Numerical results for other tunneling times, as the phase-delay time, fall within $Δτ$ . The Büttiker traversal time is the closest to $τ_p$ . Our results resemble calculations based on Feynman paths if its noisy behaviour is ignored.Exact analytical solutions of the time-dependent Schrödinger equation with the initial condition of an incident cutoff wave are used to investigate the traversal time for tunneling. The probability density starts from a vanishing value along the tunneling and transmitted regions of the potential. At the barrier width it exhibits, at early times, a distribution of traversal times that typically has a peak $τ_p$ and a width $Δτ$. Numerical results for other tunneling times, as the phase-delay time, fall within $Δτ$. The Büttiker traversal time is the closest to $τ_p$. Our results resemble calculations based on Feynman paths if its noisy behaviour is ignored.

arXiv:quant-ph/0008014Aug 3, 20000 citations

Traversal time for quantum tunneling

Ming‐Quey Chen, M.S. Wang

Physics Letters AOct 1, 199021 citations

Early times in tunneling

Jorge Villavicencio

Exact analytical solutions of the time-dependent Schrodinger equation with the initial condition of an incident cutoff wave are used to investigate the traversal time for tunneling. The probability density starts from a vanishing value along the tunneling and transmitted regions of the potential. At the barrier width it exhibits, at early times, a distribution of traversal times that typically has a peakp and a width ��. Numerical results for other tunneling times, as the phase-delay time, fall within ��. The Buttiker traversal time is the closest top. Our results resemble calculations based on Feynman paths if its noisy behaviour is ignored.Exact analytical solutions of the time-dependent Schrodinger equation with the initial condition of an incident cutoff wave are used to investigate the traversal time for tunneling. The probability density starts from a vanishing value along the tunneling and transmitted regions of the potential. At the barrier width it exhibits, at early times, a distribution of traversal times that typically has a peakp and a width ��. Numerical results for other tunneling times, as the phase-delay time, fall within ��. The Buttiker traversal time is the closest top. Our results resemble calculations based on Feynman paths if its noisy behaviour is ignored.

Aug 3, 20000 citations

Remarks on the traversal time in a tunneling process

Marco A. de Moura, Douglas F. de Albuquerque

Solid State CommunicationsMay 1, 199019 citations

τ_p

and a width

Δτ

. Numerical results for other tunneling times, as the phase-delay time, fall within

Δτ

. The Büttiker traversal time is the closest to

τ_p

. Our results resemble calculations based on Feynman paths if its noisy behaviour is ignored.