Mathematical methods in physics : distributions, Hilbert space operators and variational methods
著者
書誌事項
Mathematical methods in physics : distributions, Hilbert space operators and variational methods
（Progress in mathematical physics / editors-in-chief, Anne Boutet de Monvel, Gerald Kaiser, v. 26）
Birkhäuser, c2003
- : Boston
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注記
Includes index
内容説明・目次
内容説明
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.
目次
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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