Dwell-Time Distributions in Quantum Mechanics

Abstract

Some fundamental and formal aspects of the quantum dwell time are reviewed, examples for free motion and scattering off a potential barrier are provided, as well as extensions of the concept. We also examine the connection between the dwell time of a quantum particle in a region of space and flux-flux correlations at the boundaries, as well as operational approaches and approximations to measure the flux-flux correlation function and thus the second moment of the dwell time, which is shown to be characteristically quantum, and larger than the corresponding classical moment even for freely moving particles.

Time and quantum theory: A history and a prospectus

“…32 This operator normalized POVM returns E ∆ (R) = I and so the probability 31 See Jose Munoz et al (2010) for a recent discussion. 32 Brunetti & Fredenhagen (2002) supply a general recipe for obtaining such a POVM from any instantaneous effect which takes considerably more care with domains of definition and so on.…”

Time and energy operators in the canonical quantization of special relativity

“…It is a c-number, following Dirac's designation [1]. This is the Problem of Time (PoT) in QM, which results in the extensive discussion of the existence and meaning of a time operator [2,3], and of a time-energy uncertainty relation [4,5] in view of Pauli's objection [6].…”

“…Born acknowledges being unsuccessful in his intended applications 3 , the reciprocity principle is currently receivingrenewed interest [8][9][10]. In the present paper it is shown that it complements the required Lorentz invariance in the canonical quantization of SR to provide a unified origin for (i) the complex vector space formulation of QM; (ii) the momentum and position operators' commutation relations and their corresponding representations; (iii) the Hamiltonian in Dirac's formulation of relativistic quantum mechanics [1,[11][12][13]; (iv) the existence of a self adjoint time operator that circumvents Pauli's objection [14][15][16].…”

Manufacturing time operators: Covariance, selection criteria, and examples

“…An example of a duration is the dwell time of a particle in a region of space. The corresponding operator commutes with the Hamiltonian since the duration of a future process does not depend on the instant that we choose to predict it [5]. Instead, the other group of time observables are shifted by the same amount as the preparation time, either forward (clocks) [6] or backward (event times recorded with a stopwatch, the simplest case being the time of arrival), and are conjugate to the Hamiltonian.…”