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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Self-Adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians

Self-Adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians

Michelangeli, Alessandro
Albeverio, Sergio
Gallone, Matteo

Hardcover

Series: Springer Monographs in Mathematics

General MathematicsPhysics

ISBN10: 3031108841
ISBN13: 9783031108846
Publisher: Springer Nature
Published: Apr 5 2023
Pages: 538
Weight: 2.12
Height: 1.25 Width: 6.14 Depth: 9.21
Language: English
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.

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