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Mathematical methods in physics : distributions, Hilbert space operators, variational methods, and applications in quantum physics / Philippe Blanchard, Erwin Brüning
| Mathematical methods in physics : distributions, Hilbert space operators, variational methods, and applications in quantum physics / Philippe Blanchard, Erwin Brüning |
| Autore | Blanchard, Philippe |
| Edizione | [2. ed] |
| Pubbl/distr/stampa | [Cham], : Birkhäuser, : Springer, 2015 |
| Descrizione fisica | XXVII, 598 p. : ill. ; 24 cm |
| Altri autori (Persone) | Bruning, Erwin |
| Soggetto topico |
49-XX - Calculus of variations and optimal control; optimization [MSC 2020]
47-XX - Operator theory [MSC 2020] 46-XX - Functional analysis [MSC 2020] 81-XX - Quantum theory [MSC 2020] 81Q10 - Selfadjoint operator theory in quantum theory, including spectral analysis [MSC 2020] |
| Soggetto non controllato |
Distribution theory
Hilbert space operator Linear operators Tensor products Variational methods |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN0113332 |
Blanchard, Philippe
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| [Cham], : Birkhäuser, : Springer, 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Mathematical methods in physics : distributions, Hilbert space operators, variational methods, and applications in quantum physics / Philippe Blanchard, Erwin Brüning
| Mathematical methods in physics : distributions, Hilbert space operators, variational methods, and applications in quantum physics / Philippe Blanchard, Erwin Brüning |
| Autore | Blanchard, Philippe |
| Edizione | [2. ed] |
| Pubbl/distr/stampa | [Cham], : Birkhäuser, : Springer, 2015 |
| Descrizione fisica | XXVII, 598 p. : ill. ; 24 cm |
| Altri autori (Persone) | Bruning, Erwin |
| Soggetto topico |
46-XX - Functional analysis [MSC 2020]
47-XX - Operator theory [MSC 2020] 49-XX - Calculus of variations and optimal control; optimization [MSC 2020] 81-XX - Quantum theory [MSC 2020] 81Q10 - Selfadjoint operator theory in quantum theory, including spectral analysis [MSC 2020] |
| Soggetto non controllato |
Distribution theory
Hilbert space operator Linear operators Tensor products Variational methods |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 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 a passive process and include numerous detailed proofs, examples, and over 200 exercises, as well as hints linking mathematical concepts and results to the relevant physical concepts and theories. All of the material from the first edition has been updated, and five new chapters have been added on such topics as distributions, Hilbert space operators, and variational methods. The text is divided into three parts: - Part I: A brief introduction to (Schwartz) distribution theory. Elements from the theories of ultra distributions and (Fourier) hyperfunctions are given in addition to some deeper results for Schwartz distributions, thus providing a rather comprehensive introduction to the theory of generalized functions. Basic properties and methods for distributions are developed with applications to constant coefficient ODEs and PDEs. The relation between distributions and holomorphic functions is considered, as well as basic properties of Sobolev spaces. - Part II: Fundamental facts about Hilbert spaces. The basic theory of linear (bounded and unbounded) operators in Hilbert spaces and special classes of linear operators - compact, Hilbert-Schmidt, trace class, and Schrödinger operators, as needed in quantum physics and quantum information theory – are explored. This section also contains a detailed spectral analysis of all major classes of linear operators, including completeness of generalized eigenfunctions, as well as of (completely) positive mappings, in particular quantum operations. - Part III: Direct methods of the calculus of variations and their applications to boundary- and eigenvalue-problems for linear and nonlinear partial differential operators. The authors conclude with a discussion of the Hohenberg-Kohn variational principle. The appendices contain proofs of more general and deeper results, including completions, basic facts about metrizable Hausdorff locally convex topological vector spaces, Baire’s fundamental results and their main consequences, and bilinear functionals. Mathematical Methods in Physics is aimed at a broad community of graduate students in mathematics, mathematical physics, quantum information theory, physics and engineering, as well as researchers in these disciplines. Expanded content and relevant updates will make this new edition a valuable resource for those working in these disciplines. |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN00113332 |
|
Blanchard, Philippe
|
||
| [Cham], : Birkhäuser, : Springer, 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Means of Hilbert space operators / Fumio Hiai, Hideki Kosaki
| Means of Hilbert space operators / Fumio Hiai, Hideki Kosaki |
| Autore | Hiai, Fumio |
| Pubbl/distr/stampa | Berlin, : Springer, 2003 |
| Descrizione fisica | VIII, 148 p. ; 24 cm |
| Altri autori (Persone) | Kosaki, Hideki |
| Soggetto topico |
15A60 - Norms of matrices, numerical range, applications of functional analysis to matrix theory [MSC 2020]
47A30 - Norms (inequalities, more than one norm, etc.) of linear operators [MSC 2020] 47A64 - Operator means involving linear operators, shorted linear operators, etc. [MSC 2020] |
| Soggetto non controllato |
Double integral transformation
Hilbert Space Hilbert space operator Integral transform Interpolation Matrix theory Mean of operators Schur multiplier Unitarily invariant norm |
| ISBN | 978-35-404-0680-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN0056273 |
|
Hiai, Fumio
|
||
| Berlin, : Springer, 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Means of Hilbert space operators / Fumio Hiai, Hideki Kosaki
| Means of Hilbert space operators / Fumio Hiai, Hideki Kosaki |
| Autore | Hiai, Fumio |
| Pubbl/distr/stampa | Berlin, : Springer, 2003 |
| Descrizione fisica | VIII, 148 p. ; 24 cm |
| Altri autori (Persone) | Kosaki, Hideki |
| Soggetto topico |
15A60 - Norms of matrices, numerical range, applications of functional analysis to matrix theory [MSC 2020]
47A30 - Norms (inequalities, more than one norm, etc.) of linear operators [MSC 2020] 47A64 - Operator means involving linear operators, shorted linear operators, etc. [MSC 2020] |
| Soggetto non controllato |
Double integral transformation
Hilbert space operator Hilbert spaces Integral transform Interpolations Matrix theory Mean of operators Schur multiplier Unitarily invariant norm |
| ISBN | 978-35-404-0680-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN00056273 |
|
Hiai, Fumio
|
||
| Berlin, : Springer, 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||