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dc.contributor.authorEdwards, James
dc.contributor.authorGonzález-Domínguez, VA
dc.contributor.authorHuet, I
dc.contributor.authorTrejo, MA
dc.date.accessioned2022-11-12T16:37:11Z
dc.date.issued2022-06-28
dc.identifier.issn2470-0045
dc.identifier.issn2470-0053
dc.identifier.other064132
dc.identifier.urihttp://hdl.handle.net/10026.1/19961
dc.description.abstract

We outline an approach to calculating the quantum mechanical propagator in the presence of geometrically nontrivial Dirichlet boundary conditions. The method is based on a generalization of an integral transform of the propagator studied in previous work (the so-called “hit function”) and a convergent sequence of Padé approximants that exposes the limit of perfectly reflecting boundaries. In this paper the generalized hit function is defined as a many-point propagator, and we describe its relation to the sum over trajectories in the Feynman path integral. We then show how it can be used to calculate the Feynman propagator. We calculate analytically all such hit functions in D = 1 and D = 3 dimensions, giving recursion relations between them in the same or different dimensions and apply the results to the simple cases of propagation in the presence of perfectly conducting planar and spherical plates. We use these results to conjecture a general analytical formula for the propagator when Dirichlet boundary conditions are present in a given geometry, also explaining how it can be extended for application for more general, nonlocalized potentials. Our work has resonance with previous results obtained by Grosche in the study of path integrals in the presence of delta potentials. We indicate the eventual application in a relativistic context to determining Casimir energies using this technique.

dc.format.extent064132-
dc.format.mediumPrint
dc.languageen
dc.language.isoeng
dc.publisherAmerican Physical Society (APS)
dc.titleResummation for quantum propagators in bounded spaces
dc.typejournal-article
dc.typeJournal Article
plymouth.author-urlhttps://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000824310600004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=11bb513d99f797142bcfeffcc58ea008
plymouth.issue6
plymouth.volume105
plymouth.publication-statusPublished online
plymouth.journalPhysical Review E
dc.identifier.doi10.1103/physreve.105.064132
plymouth.organisational-group/Plymouth
plymouth.organisational-group/Plymouth/Faculty of Science and Engineering
plymouth.organisational-group/Plymouth/Faculty of Science and Engineering/School of Engineering, Computing and Mathematics
plymouth.organisational-group/Plymouth/Users by role
plymouth.organisational-group/Plymouth/Users by role/Academics
dc.publisher.placeUnited States
dcterms.dateAccepted2022-04-21
dc.rights.embargodate9999-12-31
dc.identifier.eissn2470-0053
dc.rights.embargoperiodNot known
rioxxterms.versionofrecord10.1103/physreve.105.064132
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.licenseref.startdate2022-06
rioxxterms.typeJournal Article/Review


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