國立高雄大學圖資館 |

登入

回首頁

Self-adjoint extension schemes and modern applications to quantum Hamiltonians

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Self-adjoint extension schemes and modern applications to quantum Hamiltoniansby Matteo Gallone, Alessandro Michelangeli.
作者:	Gallone, Matteo.
其他作者:	Michelangeli, Alessandro.
出版者:	Cham :Springer International Publishing :2023.
面頁冊數:	xxv, 538 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Hamiltonian systems.
電子資源:	https://doi.org/10.1007/978-3-031-10885-3
ISBN:	9783031108853$q(electronic bk.)

Self-adjoint extension schemes and modern applications to quantum Hamiltonians
Gallone, Matteo.

Self-adjoint extension schemes and modern applications to quantum Hamiltonians[electronic resource] /by Matteo Gallone, Alessandro Michelangeli. - Cham :Springer International Publishing :2023. - xxv, 538 p. :ill., digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

This 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.

ISBN: 9783031108853$q(electronic bk.)

Standard No.: 10.1007/978-3-031-10885-3doiSubjects--Topical Terms:

207807
Hamiltonian systems.

LC Class. No.: QA614.83

Dewey Class. No.: 515.39

Self-adjoint extension schemes and modern applications to quantum Hamiltonians
LDR:03236nmm a2200325 a 4500 001 643354
003 DE-He213
005 20230404090737.0
006 m d
007 cr nn 008maaau
008 231123s2023 sz s 0 eng d
020 $a 9783031108853$q(electronic bk.)
020 $a 9783031108846$q(paper)
024 7 $a 10.1007/978-3-031-10885-3 $2 doi
035 $a 978-3-031-10885-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA614.83
072 7 $a PHU $2 bicssc
072 7 $a SCI040000 $2 bisacsh
072 7 $a PHU $2 thema
082 0 4 $a 515.39 $2 23
090 $a QA614.83 $b .G173 2023
100 1 $a Gallone, Matteo. $3 951063
245 1 0 $a Self-adjoint extension schemes and modern applications to quantum Hamiltonians $h [electronic resource] / $c by Matteo Gallone, Alessandro Michelangeli.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
300 $a xxv, 538 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 2196-9922
520 $a This 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.
650 0 $a Hamiltonian systems. $3 207807
650 1 4 $a Mathematical Physics. $3 522725
650 2 4 $a Mathematical Methods in Physics. $3 273796
650 2 4 $a Analysis. $3 273775
700 1 $a Michelangeli, Alessandro. $3 791345
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Springer monographs in mathematics. $3 557774
856 4 0 $u https://doi.org/10.1007/978-3-031-10885-3
950 $a Mathematics and Statistics (SpringerNature-11649)