相关论文: Theory of Confined Quantum Time of Arrivals
We give full account of our recent report in [E.A. Galapon, R. Caballar, R. Bahague {\it Phys. Rev. Let.} {\bf 93} 180406 (2004)] where it is shown that formulating the free quantum time of arrival problem in a segment of the real line…
We show that formulating the quantum time of arrival problem in a segment of the real line suggests rephrasing the quantum time of arrival problem to finding states that evolve to unitarily collapse at a given point at a definite time. For…
The concept and the formalization of the arrival time in quantum mechanics are discussed. Different approaches based on trajectories, quantization rules, time operators, phase space techniques, renewal equations or operational procedures…
The new solution to the problem of time of arrival in quantum theory is presented herein. It allows for computer simulation of particle counters and it implies Born's interpretation. It also suggests new experiments that can answer the…
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…
A realization of the concept of "crossing state" invoked, but not implemented, by Wigner, allows to advance in two important aspects of the time of arrival in quantum mechanics: (i) For free motion, we find that the limitations described by…
Relativistic free-motion time-of-arrival theory for massive spin-1/2 particles is systematically developed. Contrary to the nonrelativistic time-of-arrival operator studied thoroughly in previous literatures, the relativistic…
Time of arrival in quantum mechanics is discussed in two versions: the classical axiomatic "time of arrival operator" introduced by J. Kijowski and the EEQT method. It is suggested that for free particles the two methods may lead to the…
A suitable operator for the time-of-arrival at a detector is defined for the free relativistic particle in 3+1 dimensions. For each detector position, there exists a subspace of detected states in the Hilbert space of solutions to the Klein…
All covariant time operators with normalized probability distribution are derived. Symmetry criteria are invoked to arrive at a unique expression for a given Hamiltonian. As an application, a well known result for the arrival time…
We introduce a formalism for the calculation of the time of arrival t at a detector of particles traveling through interacting environments. We develop a general formulation that employs quantum canonical transformations from the free to…
A relativistic version of the Aharonov-Bohm time of arrival operator for spin-0 particles was constructed by Razavi in [Il Nuovo Cimento B \textbf{63}, 271 (1969)]. We study the operator in detail by taking its rigged Hilbert space…
It is argued that the time-of-arrival cannot be precisely defined and measured in quantum mechanics. By constructing explicit toy models of a measurement, we show that for a free particle it cannot be measured more accurately then $\Delta…
We consider a number of aspects of the problem of defining time observables in quantum theory. Time observables are interesting quantities in quantum theory because they often cannot be associated with self-adjoint operators. Their…
It has always been believed that no self-adjoint and canonical time of arrival operator can be constructed within the confines of standard quantum mechanics. In this Letter we demonstrate the otherwise. We do so by pointing out that there…
Via the proper-time eigenstates (event states) instead of the proper-mass eigenstates (particle states), free-motion time-of-arrival theory for massive spin-1/2 particles is developed at the level of quantum field theory. The approach is…
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…
We reappraise and clarify the contradictory statements found in the literature concerning the time-of-arrival operator introduced by Aharonov and Bohm in Phys. Rev. {\bf 122}, 1649 (1961). We use Naimark's dilation theorem to reproduce the…
We introduce a formalism for the calculation of the time of arrival t at a space point for particles traveling through interacting media. We develop a general formulation that employs quantum canonical transformations from the free to the…
The properties of the time-of-arrival operator for free motion introduced by Aharonov and Bohm and of its self-adjoint variants are studied. The domains of applicability of the different approaches are clarified. It is shown that the…