Mathematical methods in physics : distributions, Hilbert space operators and variational methods

Bibliographic Information

Mathematical methods in physics : distributions, Hilbert space operators and variational methods

Philippe Blanchard, Erwin Brüning

(Progress in mathematical physics / editors-in-chief, Anne Boutet de Monvel, Gerald Kaiser, v. 26)

Birkhäuser, c2003

  • : Boston

Available at  / 17 libraries

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Includes index

Description and Table of Contents

Description

Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.

Table of Contents

Preface * 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 Transformation * Distributions and analytic functions * Other spaces of generalized functions * 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 bounded operators * Self-adjoint Hamilton operators * Elements of spectral theory * Spectral theory of compact operators * The spectral theorem * Some applications of the spectral representation * Introduction * The direct methods in the calculus of variations * Differential calculus on Banach spaces and extrema of differentiable functions * Constrained minimization problems (Method of Lagrange multipliers) * Boundary and eigenvalue problems * Density functional theory of atoms and molecules * Appendices * References * Index

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Details

  • NCID
    BA59854372
  • ISBN
    • 0817642285
    • 3764342285
  • Country Code
    us
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Boston
  • Pages/Volumes
    xxii, 471 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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