Space-time scattering for the Schrödinger equation View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

1998-10

AUTHORS

Arne Jensen

ABSTRACT

Results are obtained on the scattering theory for the Schrödinger equation\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i\partial _t u(t,x) = - \Delta _x u(t,x) + V(t,x)u(t,x) + F(u(t,x))$$ \end{document} in spacesLr(R;Lq(Rd)) for a certain range ofr, q, the so-called space-time scattering. In the linear case (i.e.F≡)) the relation with usual configuration space scattering is established. More... »

PAGES

363-377

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf02384775

DOI

http://dx.doi.org/10.1007/bf02384775

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1007432147


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Mathematics Institute for Electronic Systems, Aalborg University, Fredrik Bajers Vej 7E, DK-9220, Aalborg \u00d8, Denmark", 
          "id": "http://www.grid.ac/institutes/grid.5117.2", 
          "name": [
            "Department of Mathematics Institute for Electronic Systems, Aalborg University, Fredrik Bajers Vej 7E, DK-9220, Aalborg \u00d8, Denmark"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Jensen", 
        "givenName": "Arne", 
        "id": "sg:person.015240561701.11", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015240561701.11"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf01351346", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1045253666", 
          "https://doi.org/10.1007/bf01351346"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-662-03403-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030474453", 
          "https://doi.org/10.1007/978-3-662-03403-3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01459775", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1015981068", 
          "https://doi.org/10.1007/bf01459775"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/3-540-51783-9_22", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039537310", 
          "https://doi.org/10.1007/3-540-51783-9_22"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01212420", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035879795", 
          "https://doi.org/10.1007/bf01212420"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02820459", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000019495", 
          "https://doi.org/10.1007/bf02820459"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02099529", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020896184", 
          "https://doi.org/10.1007/bf02099529"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1998-10", 
    "datePublishedReg": "1998-10-01", 
    "description": "Results are obtained on the scattering theory for the Schr\u00f6dinger equation\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}\n$$i\\partial _t u(t,x) =  - \\Delta _x u(t,x) + V(t,x)u(t,x) + F(u(t,x))$$\n\\end{document} in spacesLr(R;Lq(Rd)) for a certain range ofr, q, the so-called space-time scattering. In the linear case (i.e.F\u2261)) the relation with usual configuration space scattering is established.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/bf02384775", 
    "inLanguage": "en", 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1136676", 
        "issn": [
          "0004-2080", 
          "1871-2487"
        ], 
        "name": "Arkiv f\u00f6r matematik", 
        "publisher": "International Press of Boston", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "36"
      }
    ], 
    "keywords": [
      "linear case", 
      "Schr\u00f6dinger equation", 
      "scattering theory", 
      "Schr\u00f6dinger", 
      "equations", 
      "theory", 
      "OFR", 
      "results", 
      "cases", 
      "relation", 
      "scattering", 
      "certain range ofr", 
      "range ofr", 
      "space-time scattering", 
      "usual configuration space scattering", 
      "configuration space scattering", 
      "space scattering"
    ], 
    "name": "Space-time scattering for the Schr\u00f6dinger equation", 
    "pagination": "363-377", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1007432147"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf02384775"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf02384775", 
      "https://app.dimensions.ai/details/publication/pub.1007432147"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-01-01T18:08", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_291.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/bf02384775"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/bf02384775'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf02384775'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf02384775'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf02384775'


 

This table displays all metadata directly associated to this object as RDF triples.

103 TRIPLES      22 PREDICATES      50 URIs      35 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf02384775 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N8a8be55dbe3e442ca8ae1003c0ea9e7a
4 schema:citation sg:pub.10.1007/3-540-51783-9_22
5 sg:pub.10.1007/978-3-662-03403-3
6 sg:pub.10.1007/bf01212420
7 sg:pub.10.1007/bf01351346
8 sg:pub.10.1007/bf01459775
9 sg:pub.10.1007/bf02099529
10 sg:pub.10.1007/bf02820459
11 schema:datePublished 1998-10
12 schema:datePublishedReg 1998-10-01
13 schema:description Results are obtained on the scattering theory for the Schrödinger equation\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i\partial _t u(t,x) = - \Delta _x u(t,x) + V(t,x)u(t,x) + F(u(t,x))$$ \end{document} in spacesLr(R;Lq(Rd)) for a certain range ofr, q, the so-called space-time scattering. In the linear case (i.e.F≡)) the relation with usual configuration space scattering is established.
14 schema:genre article
15 schema:inLanguage en
16 schema:isAccessibleForFree true
17 schema:isPartOf N613f122afdbc4bc9b81e929d85034ce3
18 Nc6ec2644d6354f58af287371c1517274
19 sg:journal.1136676
20 schema:keywords OFR
21 Schrödinger
22 Schrödinger equation
23 cases
24 certain range ofr
25 configuration space scattering
26 equations
27 linear case
28 range ofr
29 relation
30 results
31 scattering
32 scattering theory
33 space scattering
34 space-time scattering
35 theory
36 usual configuration space scattering
37 schema:name Space-time scattering for the Schrödinger equation
38 schema:pagination 363-377
39 schema:productId N3f671ae98fcf4dd3abadecd8874a6287
40 Nd0e251b01b4b4020ac5ecf44e20ee812
41 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007432147
42 https://doi.org/10.1007/bf02384775
43 schema:sdDatePublished 2022-01-01T18:08
44 schema:sdLicense https://scigraph.springernature.com/explorer/license/
45 schema:sdPublisher N0e850cdd1c8440728e984ad0d3166f3f
46 schema:url https://doi.org/10.1007/bf02384775
47 sgo:license sg:explorer/license/
48 sgo:sdDataset articles
49 rdf:type schema:ScholarlyArticle
50 N0e850cdd1c8440728e984ad0d3166f3f schema:name Springer Nature - SN SciGraph project
51 rdf:type schema:Organization
52 N3f671ae98fcf4dd3abadecd8874a6287 schema:name dimensions_id
53 schema:value pub.1007432147
54 rdf:type schema:PropertyValue
55 N613f122afdbc4bc9b81e929d85034ce3 schema:issueNumber 2
56 rdf:type schema:PublicationIssue
57 N8a8be55dbe3e442ca8ae1003c0ea9e7a rdf:first sg:person.015240561701.11
58 rdf:rest rdf:nil
59 Nc6ec2644d6354f58af287371c1517274 schema:volumeNumber 36
60 rdf:type schema:PublicationVolume
61 Nd0e251b01b4b4020ac5ecf44e20ee812 schema:name doi
62 schema:value 10.1007/bf02384775
63 rdf:type schema:PropertyValue
64 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
65 schema:name Mathematical Sciences
66 rdf:type schema:DefinedTerm
67 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
68 schema:name Pure Mathematics
69 rdf:type schema:DefinedTerm
70 sg:journal.1136676 schema:issn 0004-2080
71 1871-2487
72 schema:name Arkiv för matematik
73 schema:publisher International Press of Boston
74 rdf:type schema:Periodical
75 sg:person.015240561701.11 schema:affiliation grid-institutes:grid.5117.2
76 schema:familyName Jensen
77 schema:givenName Arne
78 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015240561701.11
79 rdf:type schema:Person
80 sg:pub.10.1007/3-540-51783-9_22 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039537310
81 https://doi.org/10.1007/3-540-51783-9_22
82 rdf:type schema:CreativeWork
83 sg:pub.10.1007/978-3-662-03403-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030474453
84 https://doi.org/10.1007/978-3-662-03403-3
85 rdf:type schema:CreativeWork
86 sg:pub.10.1007/bf01212420 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035879795
87 https://doi.org/10.1007/bf01212420
88 rdf:type schema:CreativeWork
89 sg:pub.10.1007/bf01351346 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045253666
90 https://doi.org/10.1007/bf01351346
91 rdf:type schema:CreativeWork
92 sg:pub.10.1007/bf01459775 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015981068
93 https://doi.org/10.1007/bf01459775
94 rdf:type schema:CreativeWork
95 sg:pub.10.1007/bf02099529 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020896184
96 https://doi.org/10.1007/bf02099529
97 rdf:type schema:CreativeWork
98 sg:pub.10.1007/bf02820459 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000019495
99 https://doi.org/10.1007/bf02820459
100 rdf:type schema:CreativeWork
101 grid-institutes:grid.5117.2 schema:alternateName Department of Mathematics Institute for Electronic Systems, Aalborg University, Fredrik Bajers Vej 7E, DK-9220, Aalborg Ø, Denmark
102 schema:name Department of Mathematics Institute for Electronic Systems, Aalborg University, Fredrik Bajers Vej 7E, DK-9220, Aalborg Ø, Denmark
103 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...