Schrödinger Equations and Diffusion Theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Springer Basel
1993
|
| Schriftenreihe: | Modern Birkhäuser Classics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Schrödinger Equations and Diffusion Theory addresses the question "What is the Schrödinger equation?" in terms of diffusion processes, and shows that the Schrödinger equation and diffusion equations in duality are equivalent. In turn, Schrödinger’s conjecture of 1931 is solved. The theory of diffusion processes for the Schrödinger equation tells us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles. The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion processes which appear to be equivalent to Schrödinger equations. The theory of large deviations and the propagation of chaos of interacting diffusion particles reveal the statistical mechanical nature of the Schrödinger equation, namely, quantum mechanics. The text is practically self-contained and requires only an elementary knowledge of probability theory at the graduate level. --- This book is a self-contained, very well-organized monograph recommended to researchers and graduate students in the field of probability theory, functional analysis and quantum dynamics. (...) what is written in this book may be regarded as an introduction to the theory of diffusion processes and applications written with the physicists in mind. Interesting topics present themselves as the chapters proceed. (...) this book is an excellent addition to the literature of mathematical sciences with a flavour different from an ordinary textbook in probability theory because of the author’s great contributions in this direction. Readers will certainly enjoy the topics and appreciate the profound mathematical properties of diffusion processes. (Mathematical Reviews) |
| Beschreibung: | 1 Online-Ressource (XII, 319 p) |
| ISBN: | 9783034805605 9783034805599 |
| DOI: | 10.1007/978-3-0348-0560-5 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042421847 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1993 |||| o||u| ||||||eng d | ||
| 020 | |a 9783034805605 |c Online |9 978-3-0348-0560-5 | ||
| 020 | |a 9783034805599 |c Print |9 978-3-0348-0559-9 | ||
| 024 | 7 | |a 10.1007/978-3-0348-0560-5 |2 doi | |
| 035 | |a (OCoLC)1184492942 | ||
| 035 | |a (DE-599)BVBBV042421847 | ||
| 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 519.2 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Nagasawa, Masao |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Schrödinger Equations and Diffusion Theory |c by Masao Nagasawa |
| 264 | 1 | |a Basel |b Springer Basel |c 1993 | |
| 300 | |a 1 Online-Ressource (XII, 319 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Modern Birkhäuser Classics | |
| 500 | |a Schrödinger Equations and Diffusion Theory addresses the question "What is the Schrödinger equation?" in terms of diffusion processes, and shows that the Schrödinger equation and diffusion equations in duality are equivalent. In turn, Schrödinger’s conjecture of 1931 is solved. The theory of diffusion processes for the Schrödinger equation tells us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles. The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion processes which appear to be equivalent to Schrödinger equations. The theory of large deviations and the propagation of chaos of interacting diffusion particles reveal the statistical mechanical nature of the Schrödinger equation, namely, quantum mechanics. The text is practically self-contained and requires only an elementary knowledge of probability theory at the graduate level. --- This book is a self-contained, very well-organized monograph recommended to researchers and graduate students in the field of probability theory, functional analysis and quantum dynamics. (...) what is written in this book may be regarded as an introduction to the theory of diffusion processes and applications written with the physicists in mind. Interesting topics present themselves as the chapters proceed. (...) this book is an excellent addition to the literature of mathematical sciences with a flavour different from an ordinary textbook in probability theory because of the author’s great contributions in this direction. Readers will certainly enjoy the topics and appreciate the profound mathematical properties of diffusion processes. (Mathematical Reviews) | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Differential equations, partial | |
| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 4 | |a Probability Theory and Stochastic Processes | |
| 650 | 4 | |a Partial Differential Equations | |
| 650 | 4 | |a Mathematical Physics | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Diffusionsprozess |0 (DE-588)4274463-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Schrödinger-Gleichung |0 (DE-588)4053332-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Diffusionsgleichung |0 (DE-588)4149816-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Diffusionsprozess |0 (DE-588)4274463-5 |D s |
| 689 | 0 | 1 | |a Schrödinger-Gleichung |0 (DE-588)4053332-3 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Schrödinger-Gleichung |0 (DE-588)4053332-3 |D s |
| 689 | 1 | 1 | |a Diffusionsgleichung |0 (DE-588)4149816-1 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-0348-0560-5 |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:BVB01-027857264 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153095363493888 |
|---|---|
| any_adam_object | |
| author | Nagasawa, Masao |
| author_facet | Nagasawa, Masao |
| author_role | aut |
| author_sort | Nagasawa, Masao |
| author_variant | m n mn |
| building | Verbundindex |
| bvnumber | BV042421847 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184492942 (DE-599)BVBBV042421847 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-0560-5 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03865nmm a2200577zc 4500</leader><controlfield tag="001">BV042421847</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1993 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783034805605</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-0348-0560-5</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783034805599</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-0348-0559-9</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-0348-0560-5</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1184492942</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042421847</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">519.2</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">Nagasawa, Masao</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Schrödinger Equations and Diffusion Theory</subfield><subfield code="c">by Masao Nagasawa</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Basel</subfield><subfield code="b">Springer Basel</subfield><subfield code="c">1993</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XII, 319 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">Modern Birkhäuser Classics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Schrödinger Equations and Diffusion Theory addresses the question "What is the Schrödinger equation?" in terms of diffusion processes, and shows that the Schrödinger equation and diffusion equations in duality are equivalent. In turn, Schrödinger’s conjecture of 1931 is solved. The theory of diffusion processes for the Schrödinger equation tells us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles. The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion processes which appear to be equivalent to Schrödinger equations. The theory of large deviations and the propagation of chaos of interacting diffusion particles reveal the statistical mechanical nature of the Schrödinger equation, namely, quantum mechanics. The text is practically self-contained and requires only an elementary knowledge of probability theory at the graduate level. --- This book is a self-contained, very well-organized monograph recommended to researchers and graduate students in the field of probability theory, functional analysis and quantum dynamics. (...) what is written in this book may be regarded as an introduction to the theory of diffusion processes and applications written with the physicists in mind. Interesting topics present themselves as the chapters proceed. (...) this book is an excellent addition to the literature of mathematical sciences with a flavour different from an ordinary textbook in probability theory because of the author’s great contributions in this direction. Readers will certainly enjoy the topics and appreciate the profound mathematical properties of diffusion processes. (Mathematical Reviews)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations, partial</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Distribution (Probability theory)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Probability Theory and Stochastic Processes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Partial Differential Equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical Physics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Diffusionsprozess</subfield><subfield code="0">(DE-588)4274463-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Schrödinger-Gleichung</subfield><subfield code="0">(DE-588)4053332-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Diffusionsgleichung</subfield><subfield code="0">(DE-588)4149816-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Diffusionsprozess</subfield><subfield code="0">(DE-588)4274463-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Schrödinger-Gleichung</subfield><subfield code="0">(DE-588)4053332-3</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="689" ind1="1" ind2="0"><subfield code="a">Schrödinger-Gleichung</subfield><subfield code="0">(DE-588)4053332-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Diffusionsgleichung</subfield><subfield code="0">(DE-588)4149816-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-0348-0560-5</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:BVB01-027857264</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><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\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.BV042421847 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9783034805605 9783034805599 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857264 |
| oclc_num | 1184492942 |
| 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, 319 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer Basel |
| record_format | marc |
| series2 | Modern Birkhäuser Classics |
| spelling | Nagasawa, Masao Verfasser aut Schrödinger Equations and Diffusion Theory by Masao Nagasawa Basel Springer Basel 1993 1 Online-Ressource (XII, 319 p) txt rdacontent c rdamedia cr rdacarrier Modern Birkhäuser Classics Schrödinger Equations and Diffusion Theory addresses the question "What is the Schrödinger equation?" in terms of diffusion processes, and shows that the Schrödinger equation and diffusion equations in duality are equivalent. In turn, Schrödinger’s conjecture of 1931 is solved. The theory of diffusion processes for the Schrödinger equation tells us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles. The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion processes which appear to be equivalent to Schrödinger equations. The theory of large deviations and the propagation of chaos of interacting diffusion particles reveal the statistical mechanical nature of the Schrödinger equation, namely, quantum mechanics. The text is practically self-contained and requires only an elementary knowledge of probability theory at the graduate level. --- This book is a self-contained, very well-organized monograph recommended to researchers and graduate students in the field of probability theory, functional analysis and quantum dynamics. (...) what is written in this book may be regarded as an introduction to the theory of diffusion processes and applications written with the physicists in mind. Interesting topics present themselves as the chapters proceed. (...) this book is an excellent addition to the literature of mathematical sciences with a flavour different from an ordinary textbook in probability theory because of the author’s great contributions in this direction. Readers will certainly enjoy the topics and appreciate the profound mathematical properties of diffusion processes. (Mathematical Reviews) Mathematics Differential equations, partial Distribution (Probability theory) Probability Theory and Stochastic Processes Partial Differential Equations Mathematical Physics Mathematik Diffusionsprozess (DE-588)4274463-5 gnd rswk-swf Schrödinger-Gleichung (DE-588)4053332-3 gnd rswk-swf Diffusionsgleichung (DE-588)4149816-1 gnd rswk-swf Diffusionsprozess (DE-588)4274463-5 s Schrödinger-Gleichung (DE-588)4053332-3 s 1\p DE-604 Diffusionsgleichung (DE-588)4149816-1 s 2\p DE-604 https://doi.org/10.1007/978-3-0348-0560-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nagasawa, Masao Schrödinger Equations and Diffusion Theory Mathematics Differential equations, partial Distribution (Probability theory) Probability Theory and Stochastic Processes Partial Differential Equations Mathematical Physics Mathematik Diffusionsprozess (DE-588)4274463-5 gnd Schrödinger-Gleichung (DE-588)4053332-3 gnd Diffusionsgleichung (DE-588)4149816-1 gnd |
| subject_GND | (DE-588)4274463-5 (DE-588)4053332-3 (DE-588)4149816-1 |
| title | Schrödinger Equations and Diffusion Theory |
| title_auth | Schrödinger Equations and Diffusion Theory |
| title_exact_search | Schrödinger Equations and Diffusion Theory |
| title_full | Schrödinger Equations and Diffusion Theory by Masao Nagasawa |
| title_fullStr | Schrödinger Equations and Diffusion Theory by Masao Nagasawa |
| title_full_unstemmed | Schrödinger Equations and Diffusion Theory by Masao Nagasawa |
| title_short | Schrödinger Equations and Diffusion Theory |
| title_sort | schrodinger equations and diffusion theory |
| topic | Mathematics Differential equations, partial Distribution (Probability theory) Probability Theory and Stochastic Processes Partial Differential Equations Mathematical Physics Mathematik Diffusionsprozess (DE-588)4274463-5 gnd Schrödinger-Gleichung (DE-588)4053332-3 gnd Diffusionsgleichung (DE-588)4149816-1 gnd |
| topic_facet | Mathematics Differential equations, partial Distribution (Probability theory) Probability Theory and Stochastic Processes Partial Differential Equations Mathematical Physics Mathematik Diffusionsprozess Schrödinger-Gleichung Diffusionsgleichung |
| url | https://doi.org/10.1007/978-3-0348-0560-5 |
| work_keys_str_mv | AT nagasawamasao schrodingerequationsanddiffusiontheory |