Time problem in quantum mechanics and weak measurements

The arrival time probability distribution is defined by analogy with the classical mechanics. The difficulty of requirement to have the values of non-commuting operators is circumvented using the concept of weak measurements. The proposed procedure is suitable to the free particles and to the particles subjected to an external potential, as well. It is shown that such an approach imposes an inherent limitation to the accuracy of the arrival time determination.

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“…We take the operator describing the interaction between the particle and the detector of the form [17,26,27]…”

Section: Weak Measurementmentioning

confidence: 99%

Weak measurement of arrival time

Ruseckas

Kaulakys

2002

Phys. Rev. A

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“…We take the operator describing the interaction between the particle and the detector of the form [22,23,[25][26][27][28]]…”

Section: The Concept Of Weak Measurementsmentioning

confidence: 99%

“…Later, for simplicity we shall neglect the Hamiltonian of the detector. Then, the evolution operator in the first-order approximation is [22] …”

Section: The Concept Of Weak Measurementsmentioning

confidence: 99%

“…(3) and (6), in the first-order approximation we obtain the mean value of A on condition that the system has the given value of B (for analogy, see [22])…”

Section: The Concept Of Weak Measurementsmentioning

confidence: 99%

“…Second, since in the classical mechanics all quantities can have definite values simultaneously, weak measurements give the correct classical limit. The concept of weak measurements has been al-ready applied to the time problem in quantum mechanics [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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Time problem in quantum mechanics and its analysis by the concept of weak measurements

Ruseckas¹,

Kaulakys²

2004

Lith. J. Phys.

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The model of weak measurements is applied to various problems, related to the time problem in quantum mechanics. The review and generalization of the theoretical analysis of the time problem in quantum mechanics based on the concept of weak measurements are presented. A question of the time interval the system spends in the specified state, when the final state of the system is given, is raised. Using the concept of weak measurements the expression for such time is obtained. The results are applied to the tunnelling problem. A procedure for the calculation of the asymptotic tunnelling and reflection times is proposed. Examples for δ-form and rectangular barrier illustrate the obtained results. Using the concept of weak measurements the arrival time probability distribution is defined by analogy with the classical mechanics. The proposed procedure is suitable to the free particles and to particles subjected to an external potential, as well. It is shown that such an approach imposes an inherent limitation to the accuracy of the arrival time definition.

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