2017
DOI: 10.1103/physreva.96.020101
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Quantum interference of position and momentum: A particle propagation paradox

Abstract: Optimal simultaneous control of position and momentum can be achieved by maximizing the probabilities of finding their experimentally observed values within two well-defined intervals. The assumption that particles move along straight lines in free space can then be tested by deriving a lower limit for the probability of finding the particle in a corresponding spatial interval at any intermediate time t. Here, it is shown that this lower limit can be violated by quantum superpositions of states confined within… Show more

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Cited by 15 publications
(36 citation statements)
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“…A similar result can be obtained for states localized in the momentum interval |p| ≤ B/2. As shown in [15], constructive quantum interferences between two states will enhance both P (L) and P (B), resulting in a value of the probability sum that exceeds the uncertainty limit suggested by Eq. (18).…”
Section: Coefficients For Localized Quantum State Componentsmentioning
confidence: 97%
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“…A similar result can be obtained for states localized in the momentum interval |p| ≤ B/2. As shown in [15], constructive quantum interferences between two states will enhance both P (L) and P (B), resulting in a value of the probability sum that exceeds the uncertainty limit suggested by Eq. (18).…”
Section: Coefficients For Localized Quantum State Componentsmentioning
confidence: 97%
“…Since the condition M is a necessary consequence of motion in a straight line for particles that satisfy both the spatial condition L and the momentum condition B, it is possible to derive an experimentally testable criterion for Newton's first law based on the probabilities of the conditions L, B, M. This condition is the particle propagation inequality introduced in [15],…”
Section: Uncertainties In the Control Of Particle Propagationmentioning
confidence: 99%
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“…Such states have not received much attention in the literature, which is not surprising given that it was hitherto unclear how to prepare them or project onto them. One exception is [42] which shows that a particle in a state like equation (5) can violate Newton's first law. The coherence between the particle's position and momentum allows for interference between the two properties.…”
Section: Joint Weak-measurementmentioning
confidence: 99%