Related papers: Time-of-arrival in quantum mechanics
We calculate the time of arrival probability distribution of a quantum particle using the Bohmian formalism. The pilot-wave is given by the wave function of the one dimensional vacuum squeezed state but written in the Schr\"odinger…
A geometric construction of the arrival time in conventional quantum mechanics is presented. It is based on a careful mathematical analysis of different quantization procedures for classical observables as functions of positions and…
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 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 extend previous work on the arrival time problem in quantum mechanics, in the framework of decoherent histories, to the case of a particle coupled to an environment. The usual arrival time probabilities are related to the probability…
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…
We introduced with coauthors some years ago a solution to the problem of time in quantum gravity which consists in formulating the quantum theory in terms of real clocks. It combines Page and Wootters' relational proposal with Rovelli's…
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…
New prescription to treat position and time equally in quantum mechanics is presented. Using this prescription, we could successfully derive some interesting formulae such as time-of-arrival for a free particle and quantum tunneling…
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…
In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat…
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…
In a previous paper [V. Delgado and J. G. Muga, Phys. Rev. A 56, 3425 (1997)] we introduced a self-adjoint operator $\hat {{\cal T}}(X)$ whose eigenstates can be used to define consistently a probability distribution of the time of arrival…
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…
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…
Quantum mechanics postulates the existence of states determined by a particle position at a single time. This very concept, in conjunction with superposition, induces much of the quantum-mechanical structure. In particular, it implies the…
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…
In the arrival time problem in quantum mechanics, a standard formula that frequently emerges as the probability for crossing the origin during a given time interval is the current integrated over that time interval. This is semiclassically…
For a quantum-mechanically spread-out particle we investigate a method for determining its arrival time at a specific location. The procedure is based on the emission of a first photon from a two-level system moving into a laser-illuminated…
The existence of a hermitian time operator is proposed in the framework of non-relativistic quantum mechanics.The Heisenberg equation of motion is shown to yield constant rate of flow of time.It is shown to yield results consistent with…