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Quantizations of the classical time of arrival and their dynamics

Eric A. Galapon, John Jaykel P. Magadan

arXiv:1804.03344Annals of PhysicsAug 23, 201821 citations

The classical limit in weyl quantization

M. A. Antonets

Functional Analysis and Its ApplicationsJan 1, 19784 citations

Classical limit of Weyl quantization

M. A. Antonets

Theoretical and Mathematical PhysicsMar 1, 197929 citations

The classical limit for Weyl quantization

M. A. Antonets

Letters in Mathematical PhysicsJan 1, 197822 citations

Instantaneous tunneling time within the theory of time-of-arrival operators

Philip Caesar Flores, Dean Alvin L. Pablico, Eric A. Galapon

It was shown in Phys. Rev. Lett. 108, 170402 (2012) that quantum tunneling is instantaneous using a time-of-arrival (TOA) operator constructed by Weyl quantization of the classical TOA. However, there are infinitely many possible quantum images of the classical TOA, leaving it unclear if one is uniquely preferred over the others. This raises the question on whether instantaneous tunneling time is simply an artifact of the chosen ordering rule. Here, we demonstrate that tunneling time vanishes for all possible quantum images of the classical arrival time, irrespective of the ordering rule between the position and momentum observables. The result still holds for TOA-operators that are constructed independent of canonical quantization, while still imposing the correct algebra defined by the time-energy canonical commutation relation.It was shown in Phys. Rev. Lett. 108, 170402 (2012) that quantum tunneling is instantaneous using a time-of-arrival (TOA) operator constructed by Weyl quantization of the classical TOA. However, there are infinitely many possible quantum images of the classical TOA, leaving it unclear if one is uniquely preferred over the others. This raises the question on whether instantaneous tunneling time is simply an artifact of the chosen ordering rule. Here, we demonstrate that tunneling time vanishes for all possible quantum images of the classical arrival time, irrespective of the ordering rule between the position and momentum observables. The result still holds for TOA-operators that are constructed independent of canonical quantization, while still imposing the correct algebra defined by the time-energy canonical commutation relation.

arXiv:2409.12389Physical Review ADec 30, 20244 citations

Quantum-classical correspondence of dynamical observables, quantization, and the time of arrival correspondence problem

Eric A. Galapon

We raise the problem of constructing quantum observables that have classical counterparts without quantization. Specifically, we seek to define and motivate a solution to the quantum-classical correspondence problem independent from quantization and discuss the general insufficiency of prescriptive quantization, particularly, the Weyl quantization. We demonstrate our points by constructing time of arrival operators without quantization and from these recover their classical counterparts.

arXiv:quant-ph/0009029Optics and SpectroscopySep 1, 200110 citations

Quantum corrections to the Weyl quantization of the classical time of arrival

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