Investigation of a quantum mechanical detector model for moving, spread-out particles

Hegerfeldt, Gerhard C.; Neumann, Jens Timo; Schulman, L. S.

doi:10.1088/0305-4470/39/46/014

Cited by 6 publications

(2 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The theoretical treatment of time observables is one of the important loose ends of quantum theory. Among them the time of arrival (TOA) has received much attention lately [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16], for earlier reviews see [17,18]. A major challenge is to find the connection between ideal TOA distributions, defined for the particle in isolation, formally independent of the measurement method, and operational ones, explicitly dependent on specific measurement models and procedures.…”

Section: Introductionmentioning

confidence: 99%

Disclosing hidden information in the quantum Zeno effect: Pulsed measurement of the quantum time of arrival

2008

View full text Add to dashboard Cite

Repeated measurements of a quantum particle to check its presence in a region of space was proposed long ago (G. R. Allcock, Ann. Phys. 53, 286 (1969)) as a natural way to determine the distribution of times of arrival at the orthogonal subspace, but the method was discarded because of the quantum Zeno effect: in the limit of very frequent measurements the wave function is reflected and remains in the original subspace. We show that by normalizing the small bits of arriving (removed) norm, an ideal time distribution emerges in correspondence with a classical local-kineticenergy distribution.

show abstract

Section: Introductionmentioning

confidence: 99%

Disclosing hidden information in the quantum Zeno effect: Pulsed measurement of the quantum time of arrival

2008

View full text Add to dashboard Cite

show abstract

“…If one is desperate to restore the conventional Hilbert space paradigm, there is an approach to arrival times in which one need not define a time operator. In practice one can measure time by measuring positions[13][14][15]. In this way the 'operator' for time becomes the collection of operators for the position measurements.…”

mentioning

confidence: 99%

Relative momentum for identical particles

Gaveau

Schulman

2012

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

Possible definitions for the relative momentum of identical particles are considered.PACS numbers: 03.65.TaThe mantra of quantum mechanics is that an observable is a self-adjoint operator and its eigenvalues are the possible results of experiments. This criterion is neither necessary nor sufficient. That it is not sufficient is manifest in the fourth chapter of Gottfried's 1966 book [1] where he points out that perfectly good operators for what are now called Schrödinger cats or grotesque states [2] are not observable. That it is not necessary one learns from that most precisely measured of physical quantities, time, which resists definition as a self-adjoint operator [3,4].In this article we find that another meaningful physical quantity, the relative momentum of identical particles, represents a further failure of the general framework. Momentum is already known to be problematic in two cases: the (single) hard wall [5] and radial momentum [6]. However, an infinite wall is an idealization and the difficulties in the second case could be attributed to the choice of coordinates. With Cartesian coordinates there is no problem.But the relative momentum of a pair of identical particles is unavoidably fundamental. The concept is not straightforward either physically or mathematically. If you cannot know which is which (more precisely, it is simply not defined), how can you attribute a vector to the difference. Mathematically, in the conventional way of dealing with identical particles one assigns identities (say #1 and #2), but works either on the space of symmetric or skewsymmetric states. However, the operator p 1 − p 2 (relative momentum) applied to a state takes you from one space to the other, and is thus not defined in the relevant Hilbert space. On the other hand, there is nothing wrong with the square of the relative momentum, nor with the squares in the examples of the previous paragraph.Physically, however, (p 1 − p 2 ) 2 is not enough. Consider an experiment on a pair of electrons. One can measure momentum with two pairs of position detectors, A and B. They are located so that it is overwhelmingly likely that energy constraints imply that the deduced p A and p B correspond to the individual electrons. The center of mass momentum, P ≡ p

show abstract