Mathematical Methods in Physics Distributions, Hilbert Space Operators, Variational Methods, and Applications in Quantum Physics /

• Κύριοι συγγραφείς: Blanchard, Philippe (Συγγραφέας), Brüning, Erwin (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.
• Έκδοση: 2nd ed. 2015.
• Σειρά: Progress in Mathematical Physics, 69
• Θέματα: Mathematics.; Functional analysis.; Operator theory.; Mathematical optimization.; Mathematical physics.; Physics.; Mathematical Physics.; Mathematical Methods in Physics.; Functional Analysis.; Operator Theory.; Optimization.

The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas.  The authors stress that learning mathematical physics is not...

Πίνακας περιεχομένων:

• Introduction
• Spaces of Test Functions
• Schwartz Distributions
• Calculus for Distributions
• Distributions as Derivatives of Functions
• Tensor Products
• Convolution Products
• Applications of Convolution
• Holomorphic Functions
• Fourier Transformations
• Distributions as Boundary Values of Analytic Functions
• Other Spaces of Generalized Functions
• Sobolev Spaces
• Hilbert Spaces: A Brief Historical Introduction
• Inner Product Spaces and Hilbert Spaces
• Geometry of Hilbert Spaces
• Separable Hilbert Spaces
• Direct Sums and Tensor Products
• Topological Aspects
• Linear Operators
• Quadratic Forms
• Bounded Linear Operators
• Special Classes of Linear Operators
• Elements of Spectral Theory
• Compact Operators
• Hilbert-Schmidt and Trace Class Operators
• The Spectral Theorem
• Some Applications of the Spectral Representation
• Spectral Analysis in Rigged Hilbert Spaces
• Operator Algebras and Positive Mappings
• Positive Mappings in Quantum Physics
• Introduction
• Direct Methods in the Calculus of Variations
• Differential Calculus on Banach Spaces and Extrema of Functions
• Constrained Minimization Problems (Method of Lagrange Multipliers)
• Boundary and Eigenvalue Problems
• Density Functional Theory of Atoms and Molecules
• Appendices
• Index.  .