The Mathematical Apparatus for Quantum-Theories: Based on the Theory of Boolean Lattices
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1966
|
| Schriftenreihe: | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete
129 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The purpose of this book is to ,give the theoretical physicist a geometrical, visual and precise mathematical apparatus which would be better adapted to some of their arguments, than the existing and generally applied methods. The theories, presented in this book, are based on the theory of Boolean lattices, whose elements are closed subspaces in the separable and complete Hilbert-Hermite-space. The first paper, in which the outlines of the said mathematical apparatus is sketched, is that of the author: "Un nouvel appareil mathematique pour la theorie des quanta."] The theory exhibited in this paper has been simplified, generalized and applied to several items of the theory of maximal normal operators in Hilbert-space, especially to the theory of multiplicity of the continuous spectrum and to permutable normal operators, based on a special canonical representation of normal operators and on a general system of coordinates in Hilbert-space, which is well adapted not only to the case of discontinuous spectrum, but also to the continuous one. The normal operators, which can be roughly characterized as operators with orthogonal eigen-vectors and complex eigen-values, constitute a generalization of hermitean selfadjoint and of unitary operators. The importance of the methods, sketched in the mentioned paper, has been emphasized in the review in the "Zentralblatt fUr Mathematik", 2 by the physicist G. LUDWIG and later applied by him in his book "Die Grundlagen der Quantenmechanik"3. The mentioned theory has 1 Annales de l'Institut HENRI POINCARE, tome XI, fasc. II, pages 49-112 |
| Beschreibung: | 1 Online-Ressource (XII, 952 p) |
| ISBN: | 9783642460302 9783642460326 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-642-46030-2 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042422497 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1966 |||| o||u| ||||||eng d | ||
| 020 | |a 9783642460302 |c Online |9 978-3-642-46030-2 | ||
| 020 | |a 9783642460326 |c Print |9 978-3-642-46032-6 | ||
| 024 | 7 | |a 10.1007/978-3-642-46030-2 |2 doi | |
| 035 | |a (OCoLC)863938216 | ||
| 035 | |a (DE-599)BVBBV042422497 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 510 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Nikodým, Otton Martin |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The Mathematical Apparatus for Quantum-Theories |b Based on the Theory of Boolean Lattices |c by Otton Martin Nikodým |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1966 | |
| 300 | |a 1 Online-Ressource (XII, 952 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |v 129 |x 0072-7830 | |
| 500 | |a The purpose of this book is to ,give the theoretical physicist a geometrical, visual and precise mathematical apparatus which would be better adapted to some of their arguments, than the existing and generally applied methods. The theories, presented in this book, are based on the theory of Boolean lattices, whose elements are closed subspaces in the separable and complete Hilbert-Hermite-space. The first paper, in which the outlines of the said mathematical apparatus is sketched, is that of the author: "Un nouvel appareil mathematique pour la theorie des quanta."] The theory exhibited in this paper has been simplified, generalized and applied to several items of the theory of maximal normal operators in Hilbert-space, especially to the theory of multiplicity of the continuous spectrum and to permutable normal operators, based on a special canonical representation of normal operators and on a general system of coordinates in Hilbert-space, which is well adapted not only to the case of discontinuous spectrum, but also to the continuous one. The normal operators, which can be roughly characterized as operators with orthogonal eigen-vectors and complex eigen-values, constitute a generalization of hermitean selfadjoint and of unitary operators. The importance of the methods, sketched in the mentioned paper, has been emphasized in the review in the "Zentralblatt fUr Mathematik", 2 by the physicist G. LUDWIG and later applied by him in his book "Die Grundlagen der Quantenmechanik"3. The mentioned theory has 1 Annales de l'Institut HENRI POINCARE, tome XI, fasc. II, pages 49-112 | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Mathematics, general | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Grundlage |0 (DE-588)4158388-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantentheorie |0 (DE-588)4047992-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Quantentheorie |0 (DE-588)4047992-4 |D s |
| 689 | 0 | 1 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 0 | 2 | |a Grundlage |0 (DE-588)4158388-7 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-642-46030-2 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027857914 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153097021292544 |
|---|---|
| any_adam_object | |
| author | Nikodým, Otton Martin |
| author_facet | Nikodým, Otton Martin |
| author_role | aut |
| author_sort | Nikodým, Otton Martin |
| author_variant | o m n om omn |
| building | Verbundindex |
| bvnumber | BV042422497 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863938216 (DE-599)BVBBV042422497 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-46030-2 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03480nmm a2200493zcb4500</leader><controlfield tag="001">BV042422497</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1966 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642460302</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-642-46030-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642460326</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-642-46032-6</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-642-46030-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863938216</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042422497</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Nikodým, Otton Martin</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The Mathematical Apparatus for Quantum-Theories</subfield><subfield code="b">Based on the Theory of Boolean Lattices</subfield><subfield code="c">by Otton Martin Nikodým</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, Heidelberg</subfield><subfield code="b">Springer Berlin Heidelberg</subfield><subfield code="c">1966</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XII, 952 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete</subfield><subfield code="v">129</subfield><subfield code="x">0072-7830</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">The purpose of this book is to ,give the theoretical physicist a geometrical, visual and precise mathematical apparatus which would be better adapted to some of their arguments, than the existing and generally applied methods. The theories, presented in this book, are based on the theory of Boolean lattices, whose elements are closed subspaces in the separable and complete Hilbert-Hermite-space. The first paper, in which the outlines of the said mathematical apparatus is sketched, is that of the author: "Un nouvel appareil mathematique pour la theorie des quanta."] The theory exhibited in this paper has been simplified, generalized and applied to several items of the theory of maximal normal operators in Hilbert-space, especially to the theory of multiplicity of the continuous spectrum and to permutable normal operators, based on a special canonical representation of normal operators and on a general system of coordinates in Hilbert-space, which is well adapted not only to the case of discontinuous spectrum, but also to the continuous one. The normal operators, which can be roughly characterized as operators with orthogonal eigen-vectors and complex eigen-values, constitute a generalization of hermitean selfadjoint and of unitary operators. The importance of the methods, sketched in the mentioned paper, has been emphasized in the review in the "Zentralblatt fUr Mathematik", 2 by the physicist G. LUDWIG and later applied by him in his book "Die Grundlagen der Quantenmechanik"3. The mentioned theory has 1 Annales de l'Institut HENRI POINCARE, tome XI, fasc. II, pages 49-112</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics, general</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Grundlage</subfield><subfield code="0">(DE-588)4158388-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Quantentheorie</subfield><subfield code="0">(DE-588)4047992-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Quantentheorie</subfield><subfield code="0">(DE-588)4047992-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Grundlage</subfield><subfield code="0">(DE-588)4158388-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-642-46030-2</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027857914</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042422497 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783642460302 9783642460326 |
| issn | 0072-7830 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857914 |
| oclc_num | 863938216 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XII, 952 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1966 |
| publishDateSearch | 1966 |
| publishDateSort | 1966 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |
| spelling | Nikodým, Otton Martin Verfasser aut The Mathematical Apparatus for Quantum-Theories Based on the Theory of Boolean Lattices by Otton Martin Nikodým Berlin, Heidelberg Springer Berlin Heidelberg 1966 1 Online-Ressource (XII, 952 p) txt rdacontent c rdamedia cr rdacarrier Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 129 0072-7830 The purpose of this book is to ,give the theoretical physicist a geometrical, visual and precise mathematical apparatus which would be better adapted to some of their arguments, than the existing and generally applied methods. The theories, presented in this book, are based on the theory of Boolean lattices, whose elements are closed subspaces in the separable and complete Hilbert-Hermite-space. The first paper, in which the outlines of the said mathematical apparatus is sketched, is that of the author: "Un nouvel appareil mathematique pour la theorie des quanta."] The theory exhibited in this paper has been simplified, generalized and applied to several items of the theory of maximal normal operators in Hilbert-space, especially to the theory of multiplicity of the continuous spectrum and to permutable normal operators, based on a special canonical representation of normal operators and on a general system of coordinates in Hilbert-space, which is well adapted not only to the case of discontinuous spectrum, but also to the continuous one. The normal operators, which can be roughly characterized as operators with orthogonal eigen-vectors and complex eigen-values, constitute a generalization of hermitean selfadjoint and of unitary operators. The importance of the methods, sketched in the mentioned paper, has been emphasized in the review in the "Zentralblatt fUr Mathematik", 2 by the physicist G. LUDWIG and later applied by him in his book "Die Grundlagen der Quantenmechanik"3. The mentioned theory has 1 Annales de l'Institut HENRI POINCARE, tome XI, fasc. II, pages 49-112 Mathematics Mathematics, general Mathematik Mathematik (DE-588)4037944-9 gnd rswk-swf Grundlage (DE-588)4158388-7 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Quantentheorie (DE-588)4047992-4 s Mathematik (DE-588)4037944-9 s Grundlage (DE-588)4158388-7 s 1\p DE-604 https://doi.org/10.1007/978-3-642-46030-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nikodým, Otton Martin The Mathematical Apparatus for Quantum-Theories Based on the Theory of Boolean Lattices Mathematics Mathematics, general Mathematik Mathematik (DE-588)4037944-9 gnd Grundlage (DE-588)4158388-7 gnd Quantentheorie (DE-588)4047992-4 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4158388-7 (DE-588)4047992-4 |
| title | The Mathematical Apparatus for Quantum-Theories Based on the Theory of Boolean Lattices |
| title_auth | The Mathematical Apparatus for Quantum-Theories Based on the Theory of Boolean Lattices |
| title_exact_search | The Mathematical Apparatus for Quantum-Theories Based on the Theory of Boolean Lattices |
| title_full | The Mathematical Apparatus for Quantum-Theories Based on the Theory of Boolean Lattices by Otton Martin Nikodým |
| title_fullStr | The Mathematical Apparatus for Quantum-Theories Based on the Theory of Boolean Lattices by Otton Martin Nikodým |
| title_full_unstemmed | The Mathematical Apparatus for Quantum-Theories Based on the Theory of Boolean Lattices by Otton Martin Nikodým |
| title_short | The Mathematical Apparatus for Quantum-Theories |
| title_sort | the mathematical apparatus for quantum theories based on the theory of boolean lattices |
| title_sub | Based on the Theory of Boolean Lattices |
| topic | Mathematics Mathematics, general Mathematik Mathematik (DE-588)4037944-9 gnd Grundlage (DE-588)4158388-7 gnd Quantentheorie (DE-588)4047992-4 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Grundlage Quantentheorie |
| url | https://doi.org/10.1007/978-3-642-46030-2 |
| work_keys_str_mv | AT nikodymottonmartin themathematicalapparatusforquantumtheoriesbasedonthetheoryofbooleanlattices |