Related papers: Time operators in stroboscopic wavepacket basis an…
A self-adjoint operator with dimensions of time is explicitly constructed, and it is shown that its complete and orthonormal set of eigenstates can be used to define consistently a probability distribution of the time of arrival at a…
We study the problem of computing the probability for the time-of-arrival of a quantum particle at a given spatial position. We consider a solution to this problem based on the spectral decomposition of the particle's (Heisenberg) state…
An operational time of arrival is introduced using a realistic position and momentum measurement scheme. The phase space measurement involves the dynamics of a quantum particle probed by a measuring device. For such a measurement an…
We formulate quantum tunneling as a time-of-arrival problem: we determine the detection probability for particles passing through a barrier at a detector located a distance L from the tunneling region. For this purpose, we use a…
We propose a time-of-arrival operator in quantum mechanics by conditioning on a quantum clock. This allows us to bypass some of the problems of previous proposals, and to obtain a Hermitian time of arrival operator whose probability…
The conundrum parameter-operator of time in quantum mechanics (QM), as well as the time-energy uncertainty relation and the tunneling delay time, have recently been addressed in attosecond optical ioniza- tion experiments. The parameter…
We model ideal arrival-time measurements for free quantum particles and for particles subject to an external interaction by means of a narrow and weak absorbing potential. This approach is related to the operational approach of measuring…
In [J. Math. Phys. 51 (2010) 022104] a self-adjoint operator was introduced that has the property that it indicates the direction of time within the framework of standard quantum mechanics, in the sense that as a function of time its…
The role of time in quantum mechanics is discussed. The differences between ordinary observables and an observable which corresponds to the time of an event is examined. In particular, the time-of-arrival of a particle to a fixed location…
Tunneling of a particle through a potential barrier is a fundamental physical process and a major thought-provoking outcome of quantum physics. It is at the basis of multiple scientific and technological advances and strongly influences…
It has been shown in Phys. Rev. Lett., 108 170402 (2012) (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.170402), that quantum tunneling is instantaneous using a time-of-arrival (TOA) operator constructed by Weyl quantization…
We provide a full account of our recent report (EPL, 141 (2023) 10001}) which constructed a quantized relativistic time-of-arrival operator for spin-0 particles using a modified Weyl-ordering rule to calculate the traversal time across a…
We analyze the tunneling time problem via the presence time formalism. With this method we reproduce previous results for very long wavepackets and we are able to calculate the tunneling time for general wavepackets of arbitrary shape and…
Time it takes to travel from one position to another, devoid of any quantum mechanical description, has been modeled variously, especially for quantum tunneling. The model time, if universally valid, must be subluminal, must hold everywhere…
Time continues to be an intriguing physical property in the modern era. On the one hand, we have the Classical and Relativistic notion of time, where space and time have the same hierarchy, which is essential in describing events in…
Stochastic systems consisting of a very large number of independent elementary processes of the same kind, especially the radioactive decay, are considered as quantum clocks. By adapting the framework of the previously introduced concept of…
We develop a general framework for the construction of probabilities for the time of arrival in quantum systems. The time of arrival is identified with the time instant when a transition in the detector's degrees of freedom takes place.…
In this work we present a re-evaluation of the concept of time in non-relativistic quantum theory. We suggest a formalism in which time is changed into the status of an operator, and where expectation values of observables and the state of…
The question of how to interpret and compute arrival-time distributions in quantum mechanics remains unsettled, reflecting the longstanding tension between treating time as a quantum observable or as a classical parameter. Most previous…
Using a time operator, we define a tunneling time for a particle going through a barrier. This tunneling time is the average of the phase time introduced by other authors. In addition to the delay time caused by the resonances over the…