Time of Arrival in Quantum Mechanics

Muga, J. G.; Brouard, S.; Macı́as, Demetrio

doi:10.1006/aphy.1995.1048

Cited by 95 publications

(98 citation statements)

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“…One can show however that these "averages" do coincide with the ones calculated with the positive definite "ideal" time-of-arrival distribution of Kijowski [37,38]. They are also in essential agreement with averages computed with localized detectors modeled by complex potentials [39,40].…”

Section: The Hartman Effect and Its Large-barrier-width Limitationsupporting

confidence: 67%

Bounds and enhancements for negative scattering time delays

et al. 2002

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The time of passage of the transmitted wave packet in a tunneling collision of a quantum particle with a square potential barrier becomes independent of the barrier width in a range of barrier thickness. This is the Hartman effect, which has been frequently associated with "superluminality". A fundamental limitation on the effect is set by non-relativistic "causality conditions". We demonstrate first that the causality conditions impose more restrictive bounds on the negative time delays (time advancements) when no bound states are present. These restrictive bounds are in agreement with a naive, and generally false, causality argument based on the positivity of the "extrapolated phase time", one of the quantities proposed to characterize the duration of the barrier's traversal. Nevertheless, square wells may in fact lead to much larger advancements than square barriers. We point out that close to thresholds of new bound states the time advancement increases considerably, while, at the same time, the transmission probability is large, which facilitates the possible observation of the enhanced time advancement.

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Section: The Hartman Effect and Its Large-barrier-width Limitationsupporting

confidence: 67%

Bounds and enhancements for negative scattering time delays

et al. 2002

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“…They also derived a least-upper-bound, estimated to be 0.04, for the time integral of |J(0, t)| over an interval of negative J(0, t). But the backflow effect is negligible quantitatively at asymptotic distances from the source or interaction region [4]. This in part explains why the arrival time is not particularly worrysome for the practitioner of time of flight or other arrival time measurement techniques.…”

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confidence: 80%

“…In general, in the absence of backflow at x = 0, the flux J(0, t) at the front edge of the detector (conventionally located between 0 and L) and −dN(t)/dt are close to each other, but the latter is slightly delayed with respect to the former because of the time it takes to absorb (i.e., to pass from the incident to the final channels) the part of the wave inside the detector. More precisely, the time averages evaluated with J(0, t) and −dN(t)/dt differ by the mean dwell time in the detector τ D [4]. The arrival time distribution is in this context defined operationally, it depends on the apparatus, and it is given by the absorption rate −dN(t)/dt (suitably normalized to account for any incident particles that do not reach the detector).…”

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confidence: 99%

“…Despite this there are experiments, most notably "time of flight experiments", that seemingly circumvent the theoretical objections and difficulties exemplified by Allcock's work [1]. Several researchers have tried in recent years to fill this gap between theory and practice by reexamining the subject using a variety of approaches [2][3][4][5][6][7][8][9][10][11][12][13][14]; a recent review provides a brief summary of the methods applied and a discussion of open questions [14].…”

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Arrival time distributions and perfect absorption in classical and quantum mechanics

1999

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“…These states are the same eigenstates (with positive and negative momentum) as the time-of-arrival operator defined by adding the symmetrization and quantization of the classical expression mx class /p class to conventional QM. This operator was first defined by Aharonov and Bohm [28], and later used by several other authors (see, for instance, [3,10,29]). …”

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Space-time-symmetric extension of nonrelativistic quantum mechanics

Dias

Parisio

2017

Phys. Rev. A

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In quantum theory we refer to the probability of finding a particle between positions x and x + dx at the instant t, although we have no capacity of predicting exactly when the detection occurs. In this work, first we present an extended non-relativistic quantum formalism where space and time play equivalent roles. It leads to the probability of finding a particle between x and x + dx during [t,t + dt]. Then, we find a Schrödinger-like equation for a "mirror" wave function φ(t, x) associated with the probability of measuring the system between t and t + dt, given that detection occurs at x. In this framework, it is shown that energy measurements of a stationary state display a non-zero dispersion, and that energy-time uncertainty arises from first principles. We show that a central result on arrival time, obtained through approaches that resort to ad hoc assumptions, is a natural, built-in part of the formalism presented here. In Schrödinger quantum mechanics (QM) there is a clear asymmetry between time and space. Time is a continuous parameter that can be chosen with arbitrary precision and used to label the solution of the wave equation. In contrast, the position of a particle is seen as an operator, and therefore its value under a measurement is inherently probabilistic. It is common to hear that this asymmetry is due to the non-relativistic character of the Schrödinger equation (SE). Although partially correct, this argument is largely insufficient to justify all the disparity between space and time in the formalism of QM.A clear illustration is as follows. In a position measurement, ψ(x, t) = x|ψ(t) gives the probability amplitude of finding the particle within [x, x + dx], given that the time of detection is t. Would it not be equally reasonable, even in the non-relativistic domain, to ask about the probability of measuring the particle between x and x + dx, and t and t + dt? In this broader scenario, inquiring about the state of a particle at a given time t (as we often do), should make as much sense as asking about the state of that particle in a given position x (which we never do). In addition, if symmetry is to hold at this level, then there should exist a "mirror" wave function φ(t, x) = t|φ(x) , where x is a continuous parameter and t is the eigenvalue of an observable. If the location of particle becomes a physical reality only when a measurement is made, then it is a tenable position to expect that time should emerge in the same way. To earnestly consider these issues is the main goal of this manuscript.Time has been addressed in different contexts in QM . Common to several of these works is the attempt to remain within the borders of the standard theory. However, the solution to the arrival-time problem is considered by several authors to lay outside the framework of QM. It concerns the arrival of a particle in a spatially localized apparatus, where a time operator may be defined so that the relation [T ,Ĥ] = i is satisfied, and * corresponding author: eduardodias@df.ufpe.br † parisio@df.ufpe.br ...

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Time of Arrival in Quantum Mechanics

Cited by 95 publications

References 0 publications

Bounds and enhancements for negative scattering time delays

Bounds and enhancements for negative scattering time delays

Arrival time distributions and perfect absorption in classical and quantum mechanics

Space-time-symmetric extension of nonrelativistic quantum mechanics

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