Intermediate Spectral Theory and Quantum Dynamics

• Main Author: Oliveira, Cšar R. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Basel : Birkhũser Basel, 2009.
• Series: Progress in Mathematical Physics ; 54
• Subjects: Physics.; Quantum theory.; Mathematical physics.; Quantum Physics.; Mathematical Methods in Physics.; Physics, general.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-7643-8795-2

The spectral theory of linear operators plays a key role in the mathematical formulation of quantum theory. Furthermore, such a rigorous mathematical foundation leads to a more profound insight into the nature of quantum mechanics. This textbook provides a concise and comprehensible introduction to...

Table of Contents:

• 1 Linear Operators and Spectrum
• 2 Adjoint Operator
• 3 Fourier Transform and Free Hamiltonian
• 4 Operators via Sesquilinear Forms
• 5 Unitary Evolution Groups
• 6 Kato-Rellich Theorem
• 7 Boundary Triples and Self-Adjointness
• 8 Spectral Theorem
• 9 Applications of the Spectral Theorem
• 10 Convergence of Self-Adjoint Operators
• 11 Spectral Decomposition I
• 12 Spectral Decomposition II
• 13 Spectrum and Quantum Dynamics
• 14 Some Quantum Relations.