相关论文: Space-time properties of free motion time-of-arriv…
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…
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…
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…
Although one can show formally that a time-of-arrival operator cannot exist, one can modify the low momentum behaviour of the operator slightly so that it is self-adjoint. We show that such a modification results in the difficulty that 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…
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…
Previous numerical analyses on the Aharonov-Bohm (AB) operator representing the quantum time-of-arrival (TOA) observable for the free particle have indicated that its eigenfunctions represent quantum states with definite arrival time at the…
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…
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 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…
It is shown that in presence of certain external fields a well defined self-adjoint time operator exists, satisfying the standard canonical commutation relations with the Hamiltonian. Examples include uniform electric and gravitational…
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…
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…
We develop a new conception for the quantum mechanical arrival time distribution from the perspective of Bohmian mechanics. A detection probability for detectors sensitive to quite arbitrary spacetime domains is formulated. Basic positivity…
We demonstrate that the time operator that measures the time of arrival of a quantum particle into chosen state can be defined as a self-adjoint quantum-mechanical operator using periodic boundary conditions on applied to wavefuncions in…
We construct a one-particle TOA operator $\mathcal{\hat{T}}$ canonically conjugate with the Hamiltonian describing a free, charged, spin-$0$, relativistic particle in one spatial dimension and show that it is maximally symmetric. We solve…
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 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…
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…
We extend the concept of confined quantum time of arrival operators, first developed for the free particle [E.A. Galapon, R. Caballar, R. Bahague {\it Phys. Rev. Let.} {\bf 93} 180406 (2004)], to arbitrary potentials.