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

Philippe Blanchard, Erwin Brüning

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.

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[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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この本の情報

書名 Mathematical methods in physics : distributions, Hilbert space operators and variational methods
著作者等 Blanchard, Philippe
Brüning, Erwin
Bruening Erwin
シリーズ名 Progress in mathematical physics
出版元 Birkhäuser
刊行年月 c2003
ページ数 xxii, 471 p.
大きさ 24 cm
ISBN 3764342285
0817642285
NCID BA59854372
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言語 英語
出版国 アメリカ合衆国
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