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Mathematical Methods in Physics Distributions, Hilbert Space Operators, Variational Methods, and Applications in Quantum Physics /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Birkhäuser,
2015.
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| Edición: | 2nd ed. 2015. |
| Colección: | Progress in Mathematical Physics,
69 |
| Temas: | |
| Acceso en línea: | Texto Completo |
Tabla de Contenidos:
- 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. .