LEADER 04045nam 2200517 450 001 9910686787203321 005 20230731000050.0 010 $a9783031108853$b(electronic bk.) 010 $z9783031108846 024 7 $a10.1007/978-3-031-10885-3 035 $a(MiAaPQ)EBC7233706 035 $a(Au-PeEL)EBL7233706 035 $a(OCoLC)1376193768 035 $a(DE-He213)978-3-031-10885-3 035 $a(PPN)269655603 035 $a(EXLCZ)9926388128800041 100 $a20230731d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSelf-Adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians /$fMatteo Gallone and Alessandro Michelangeli ; foreword by Sergio Albeverio 205 $aFirst edition. 210 1$aCham, Switzerland :$cSpringer Nature Switzerland AG,$d[2023] 210 4$dİ2023 215 $a1 online resource (557 pages) 225 1 $aSpringer Monographs in Mathematics Series 311 08$aPrint version: Gallone, Matteo Self-Adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians Cham : Springer International Publishing AG,c2023 9783031108846 320 $aIncludes bibliographical references and index. 330 $aThis book introduces and discusses the self-adjoint extension problem for symmetric operators on Hilbert space. It presents the classical von Neumann and Krein?Vishik?Birman extension schemes both in their modern form and from a historical perspective, and provides a detailed analysis of a range of applications beyond the standard pedagogical examples (the latter are indexed in a final appendix for the reader?s convenience). Self-adjointness of operators on Hilbert space representing quantum observables, in particular quantum Hamiltonians, is required to ensure real-valued energy levels, unitary evolution and, more generally, a self-consistent theory. Physical heuristics often produce candidate Hamiltonians that are only symmetric: their extension to suitably larger domains of self-adjointness, when possible, amounts to declaring additional physical states the operator must act on in order to have a consistent physics, and distinct self-adjoint extensions describe different physics. Realising observables self-adjointly is the first fundamental problem of quantum-mechanical modelling. The discussed applications concern models of topical relevance in modern mathematical physics currently receiving new or renewed interest, in particular from the point of view of classifying self-adjoint realisations of certain Hamiltonians and studying their spectral and scattering properties. The analysis also addresses intermediate technical questions such as characterising the corresponding operator closures and adjoints. Applications include hydrogenoid Hamiltonians, Dirac?Coulomb Hamiltonians, models of geometric quantum confinement and transmission on degenerate Riemannian manifolds of Grushin type, and models of few-body quantum particles with zero-range interaction. Graduate students and non-expert readers will benefit from a preliminary mathematical chapter collecting all the necessary pre-requisites on symmetric and self-adjoint operators on Hilbert space (including the spectral theorem), and from a further appendix presenting the emergence from physical principles of the requirement of self-adjointness for observables in quantum mechanics. 410 0$aSpringer monographs in mathematics. 606 $aMathematical physics 606 $aMathematical analysis 615 0$aMathematical physics. 615 0$aMathematical analysis. 676 $a530.15 700 $aGallone$b Matteo$01349774 702 $aMichelangeli$b Alessandro 702 $aAlbeverio$b Sergio 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910686787203321 996 $aSelf-Adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians$93418010 997 $aUNINA