Self-adjoint Extensions in Quantum Mechanics General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials /

• Main Authors: Gitman, D.M (Author), Tyutin, I.V (Author), Voronov, B.L (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston : Birkhäuser Boston, 2012.
• Series: Progress in Mathematical Physics ; 62
• Subjects: Mathematics.; Operator theory.; Applied mathematics.; Engineering mathematics.; Mathematical physics.; Physics.; Quantum physics.; Mathematical Physics.; Mathematical Methods in Physics.; Operator Theory.; Quantum Physics.; Applications of Mathematics.

Quantization of physical systems requires a correct definition of quantum-mechanical observables, such as the Hamiltonian, momentum, etc., as self-adjoint operators in appropriate Hilbert spaces and their spectral analysis.  Though a “naïve”  treatment exists for dealing with such problems, it is ba...

Table of Contents:

• Introduction
• Linear Operators in Hilbert Spaces
• Basics of Theory of s.a. Extensions of Symmetric Operators
• Differential Operators
• Spectral Analysis of s.a. Operators
• Free One-Dimensional Particle on an Interval
• One-Dimensional Particle in Potential Fields
• Schrödinger Operators with Exactly Solvable Potentials
• Dirac Operator with Coulomb Field
• Schrödinger and Dirac Operators with Aharonov-Bohm and Magnetic-Solenoid Fields.