In this paper we develop and refine our recent model of a one-dimensional completed scattering, which gives an individual description of the transmission and reflection subprocesses at all stages of scattering. We show that the group, dwell and Larmor characteristic times, introduced in this model for the subprocesses, are in a full agreement with special relativity and allow us to solve the Hartman effect puzzle.
In this paper we develop and refine our recent model of a one-dimensional completed scattering, which gives an individual description of the transmission and reflection subprocesses at all stages of scattering. We show that the group, dwell and Larmor characteristic times, introduced in this model for the subprocesses, are in a full agreement with special relativity and allow us to solve the Hartman effect puzzle.
We develop a new quantum-mechanical approach to scattering a particle on a one-dimensional (1D) system of two identical rectangular potential barriers, which implies modelling the dynamics of its subprocesses -- transmission and reflection -- at all stages of scattering. On its basis we define, for each subprocess, the dwell time as well as the local (exact) and asymptotic (extrapolated) group times. Our concept of the asymptotic transmission group time confirms the validity of the Wigner phase time in the opaque limit, as well as the existence of the usual and generalized Hartman effects predicted on its basis. On the energy scale, this concept is valid everywhere in the high energy region as well as in the low energy region, excepting resonance points and their neighborhoods. On the contrary, the Buttiker dwell time is valid, as the transmission time, just only at the resonance points. Our concept of the transmission dwell time predicts monotonous growth of the tunneling time when the distance between the opaque barriers increases. By our approach only this time scale yields the true time spent, on average, by transmitted particles in the region occupied by the system. We explain why the asymptotic and local transmission group times cannot play this role and why the concept of {\it transmission group} velocity lies beyond the scope of special relativity. And else, all the transmission times admit only indirect measurements. Hence the unambiguous interpretation of all tunneling-time experiments is impossible when the transmission dynamics at all stages of scattering is unknown.
We develop a new quantum-mechanical approach to scattering a particle on a one-dimensional (1D) system of two identical rectangular potential barriers, which implies modelling the dynamics of its subprocesses -- transmission and reflection -- at all stages of scattering. On its basis we define, for each subprocess, the dwell time as well as the local (exact) and asymptotic (extrapolated) group times. Our concept of the asymptotic transmission group time confirms the validity of the Wigner phase time in the opaque limit, as well as the existence of the usual and generalized Hartman effects predicted on its basis. On the energy scale, this concept is valid everywhere in the high energy region as well as in the low energy region, excepting resonance points and their neighborhoods. On the contrary, the Buttiker dwell time is valid, as the transmission time, just only at the resonance points. Our concept of the transmission dwell time predicts monotonous growth of the tunneling time when the distance between the opaque barriers increases. By our approach only this time scale yields the true time spent, on average, by transmitted particles in the region occupied by the system. We explain why the asymptotic and local transmission group times cannot play this role and why the concept of {\it transmission group} velocity lies beyond the scope of special relativity. And else, all the transmission times admit only indirect measurements. Hence the unambiguous interpretation of all tunneling-time experiments is impossible when the transmission dynamics at all stages of scattering is unknown.
A {\it completed} scattering of a particle on a static one-dimensional (1D) potential barrier is a combined quantum process to consist from two elementary sub-processes (transmission and reflection) evolved coherently at all stages of scattering and macroscopically distinct at the final stage. The existing model of the process is clearly inadequate to its nature: all one-particle "observables" and "tunneling times", introduced as quantities to be common for the sub-processes, cannot be experimentally measured and, consequently, have no physical meaning; on the contrary, quantities introduced for either sub-process have no basis, for the time evolution of either sub-process is unknown in this model. We show that the wave function to describe a completed scattering can be uniquely presented as the sum of two solutions to the Schrödinger equation, which describe separately the sub-processes at all stages of scattering. For symmetric potential barriers such solutions are found explicitly. For either sub-process we define the time spent, on the average, by a particle in the barrier region. We define it as the Larmor time. As it turned out, this time is just Buttiker's dwell time averaged over the corresponding localized state. Thus, firstly, we justify the known definition of the local dwell time introduced by Hauge and co-workers as well by Leavens and Aers, for now this time can be measured; secondly, we confirm that namely Buttiker's dwell time gives the energy-distribution for the tunneling time; thirdly, we state that all the definitions are valid only if they are based on the wave functions for transmission and reflection found in our paper. Besides, we define the exact and asymptotic group times to be auxiliary in timing the scattering process.
A new approach to the problem of scattering the plane electromagnetic TE wave on a homogeneous dielectric layer is presented, which does not predict, unlike the standard model, the Hartman effect for the tunneling time in the case of scattering the TE wave in the regime of a frustrated total internal refection (FTIR). The basic idea of this approach is that a correct definition of the tunneling velocity and time is possible if only the dynamics of both its subprocesses — transmission and reflection — is known at all stages of the scattering process investigated. It is shown that the Wigner (group) tunneling time was introduced without taking into account of this requirement, and, as a consequence, both this characteristic itself and the associated with it Hartman effect have no relation to transferring the light energy through the layer. The dwell transmission time, which is directly related to it, does not lead to the Hartman effect.
In a recent review paper [Phys. Rpeorts 214 (1992) 339] we proposed, within conventional quantum mechanics, new definitions fot the subarrier tunnelling and reflection times. Aims of the present paper are: (i) presenting and analysing the results of various numerical calculations (based on our equations) on the penetration and return times $\\left \\langle tau_P_e_n \\right \\rangle $ , $\\left \\langle tau_R_e_t\\right \\rangle $ during tunnelling inside a rectangular potential barrier, for various penetration depths xf ; (ii) putting forth and discussing suitable definitions. Besides of the mean values, also of the variances (or dispersions)$D\\tau_T\\ $ and $ D\\tau_R\\ $ for the tima durations of trasmission and reflection processes; (iii) mentioning that our definition $\\left \\langle tau_T \\right \\rangle $ for the average transmission time results to constituite an improvemente of the ordinary dwell-time $ \\bar tau^D^W\\ $ formula: (iv) commenting upon some recent criticism by C.R. Leavens, on the basis of our new numerical results. We stress that our numerical evaluations confirm that our approach implied, and implies, the existence of the Hartman effect: an effect that in these days (due to the theoretical connections between tunnelling and evanescent-wave propagation) is receiving - at Cologne, Berkeley, Florence and Wien - indirect, but quite interesting, experimental verifications. At last we briefly analyze some other definitions of tunnelling times.
In a recent review paper [{\em Phys. Reports} {\bf 214} (1992) 339] we proposed, within conventional quantum mechanics, new definitions for the sub-barrier tunnelling and reflection times. \ Aims of the present paper are: \ (i) presenting and analysing the results of various numerical calculations (based on our equations) on the penetration and return times ,, during tunnelling {\em inside} a rectangular potential barrier, for various penetration depths xf; \ (ii) putting forth and discussing suitable definitions, besides of the mean values, also of the {\em variances} (or dispersions) DτT and DτR for the time durations of transmission and reflection processes; \ (iii) mentioning, moreover, that our definition $$ for the average transmission time results to constitute an {\em improvement} of the ordinary dwell--time ${\ove τ}^{\rm Dw}$ formula: \ (iv) commenting, at last, on the basis of our {\em new} numerical results, upon some recent criticism by C.R.Leavens. \ \ We stress that our numerical evaluations {\em confirm} that our approach implied, and implies, the existence of the {\em Hartman effect}: an effect that in these days (due to the theoretical connections between tunnelling and evanescent--wave propagation) is receiving ---at Cologne, Berkeley, Florence and Vienna--- indirect, but quite interesting, experimental verifications. \ Eventually, we briefly analyze some other definitions of tunnelling times.