LEADER 06193nam 22007455 450 001 9910299763703321 005 20200630160920.0 010 $a3-319-14045-0 024 7 $a10.1007/978-3-319-14045-2 035 $a(CKB)3710000000404014 035 $a(SSID)ssj0001501592 035 $a(PQKBManifestationID)11799485 035 $a(PQKBTitleCode)TC0001501592 035 $a(PQKBWorkID)11446210 035 $a(PQKB)10830353 035 $a(DE-He213)978-3-319-14045-2 035 $a(MiAaPQ)EBC5590724 035 $a(PPN)185489680 035 $a(EXLCZ)993710000000404014 100 $a20150407d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical Methods in Physics$b[electronic resource] $eDistributions, Hilbert Space Operators, Variational Methods, and Applications in Quantum Physics /$fby Philippe Blanchard, Erwin Brüning 205 $a2nd ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2015. 215 $a1 online resource (XXVII, 598 p. 4 illus.) 225 1 $aProgress in Mathematical Physics,$x1544-9998 ;$v69 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-14044-2 327 $aIntroduction -- 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.  . 330 $aThe 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 main parts. Part I is a brief introduction to distribution theory, in which elements from the theories of ultradistributions and hyperfunctions are considered in addition to some deeper results for Schwartz distributions, thus providing a comprehensive introduction to the theory of generalized functions. Part II contains fundamental facts about Hilbert spaces and their geometry. The theory of linear operators, both bounded and unbounded, is developed, focusing on results needed for the theory of Schrödinger operators. Part III treats the direct methods of the calculus of variations and their applications to boundary- and eigenvalue-problems for linear and nonlinear partial differential operators. 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. 410 0$aProgress in Mathematical Physics,$x1544-9998 ;$v69 606 $aMathematical physics 606 $aPhysics 606 $aFunctional analysis 606 $aOperator theory 606 $aMathematical optimization 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aOptimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26008 615 0$aMathematical physics. 615 0$aPhysics. 615 0$aFunctional analysis. 615 0$aOperator theory. 615 0$aMathematical optimization. 615 14$aMathematical Physics. 615 24$aMathematical Methods in Physics. 615 24$aFunctional Analysis. 615 24$aOperator Theory. 615 24$aOptimization. 676 $a530.15 700 $aBlanchard$b Philippe$4aut$4http://id.loc.gov/vocabulary/relators/aut$0345681 702 $aBrüning$b Erwin$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299763703321 996 $aMathematical Methods in Physics$92507092 997 $aUNINA