Physics – Quantum Physics
Scientific paper
1996-03-14
Phys.Rev. A54 (1996) 4679
Physics
Quantum Physics
Latex/Revtex, 20 pages. 2 figs included using epsf. Submitted to Phys. Rev. A
Scientific paper
10.1103/PhysRevA.54.4676
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 into the eigenstates of a suitable operator, which we denote as the ``time-of-arrival'' operator. We discuss the general properties of this operator. We construct the operator explicitly in the simple case of a free nonrelativistic particle, and compare the probabilities it yields with the ones estimated indirectly in terms of the flux of the Schr\"odinger current. We derive a well defined uncertainty relation between time-of-arrival and energy; this result shows that the well known arguments against the existence of such a relation can be circumvented. Finally, we define a ``time-representation'' of the quantum mechanics of a free particle, in which the time-of-arrival is diagonal. Our results suggest that, contrary to what is commonly assumed, quantum mechanics exhibits a hidden equivalence between independent (time) and dependent (position) variables, analogous to the one revealed by the parametrized formalism in classical mechanics.
Grot Norbert
Rovelli Carlo
Tate Ranjeet S.
No associations
LandOfFree
Time-of-arrival in quantum mechanics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Time-of-arrival in quantum mechanics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Time-of-arrival in quantum mechanics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-340506