[1807.03800] Position Measurement-Induced Collapse: A Unified Quantum Description of Fraunhofer and Fresnel Diffractions Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:1807.03800 (quant-ph) [Submitted on 10 Jul 2018 ( v1 ), last revised 10 Aug 2018 (this version, v2)] Title: Position Measurement-Induced Collapse: A Unified Quantum Description of Fraunhofer and Fresnel Diffractions Authors: Moncy V John , Kiran Mathew View a PDF of the paper titled Position Measurement-Induced Collapse: A Unified Quantum Description of Fraunhofer and Fresnel Diffractions, by Moncy V John and Kiran Mathew View PDF HTML (experimental) Abstract: Position measurement-induced collapse states are shown to provide a unified quantum description of diffraction of particles passing through a single slit. These states, which we here call `quantum location states', are represented by the conventional rectangular wave function at the initial moment of position measurement. We expand this state in terms of the position eigenstates, which in turn can be represented as a linear combination of energy eigenfunctions of the problem, using the closure property. The time-evolution of the location states in the case of free particles is shown to have position probability density patterns closely resembling diffraction patterns in the Fresnel region for small times and the same in Fraunhofer region for large times. Using the quantum trajectory representations in the de Broglie-Bohm, modified de Broglie-Bohm and Floyd-Faraggi-Matone formalisms, we show that Fresnel and Fraunhofer diffractions can be described using a single expression. We also discuss how to obtain the probability density of location states for the case of particles moving in a general potential, detected at some arbitrary point. In the case of the harmonic oscillator potential, we find that they have oscillatory properties similar to that of coherent states. Comments: Minor changes Subjects: Quantum Physics (quant-ph) ; Optics (physics.optics) Cite as: arXiv:1807.03800 [quant-ph] (or arXiv:1807.03800v2 [quant-ph] for this version) https://doi.org/10.48550/arXiv.1807.03800 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Foundations of Physics (2019) Related DOI : https://doi.org/10.1007/s10701-019-00248-0 Focus to learn more DOI(s) linking to related resources Submission history From: Moncy Vilavinal John [ view email ] [v1] Tue, 10 Jul 2018 18:01:12 UTC (111 KB) [v2] Fri, 10 Aug 2018 16:34:16 UTC (118 KB) Full-text links: Access Paper: View a PDF of the paper titled Position Measurement-Induced Collapse: A Unified Quantum Description of Fraunhofer and Fresnel Diffractions, by Moncy V John and Kiran Mathew View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2018-07 Change to browse by: physics physics.optics References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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