The first solution of a long standing problem: Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrödinger equation
Abstract A long standing problem is completely solved here for the first time. This problem was posed by K. Chadan and P. C. Sabatier in their classical book “Inverse Problems in Quantum Scattering Theory”, Springer, New York, 1977. The inverse scattering problem of the reconstruction of the unknown...
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Gespeichert in:
| Autor*in: |
Klibanov, Michael V. [verfasserIn] |
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| Format: |
Artikel |
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| Erschienen: |
2015 |
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| Anmerkung: |
© 2015 by De Gruyter |
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| Übergeordnetes Werk: |
Enthalten in: Journal of inverse and ill-posed problems - De Gruyter, 1993, 23(2015), 4 vom: 21. Mai, Seite 415-428 |
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| Übergeordnetes Werk: |
volume:23 ; year:2015 ; number:4 ; day:21 ; month:05 ; pages:415-428 |
| Links: |
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| DOI / URN: |
10.1515/jiip-2015-0025 |
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OLC2138269671 |
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| 520 | |a Abstract A long standing problem is completely solved here for the first time. This problem was posed by K. Chadan and P. C. Sabatier in their classical book “Inverse Problems in Quantum Scattering Theory”, Springer, New York, 1977. The inverse scattering problem of the reconstruction of the unknown potential with a compact support in the three-dimensional Schrödinger equation is considered. Only the modulus of the scattering complex-valued wave field is known, whereas the phase is unknown. It is shown that the unknown potential can be reconstructed via the inverse Radon transform. This solution has potential applications in imaging of nanostructures. | ||
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10.1515/jiip-2015-0025 doi (DE-627)OLC2138269671 (DE-B1597)jiip-2015-0025-p DE-627 ger DE-627 rakwb 510 VZ 510 VZ 11 ssgn Klibanov, Michael V. verfasserin aut The first solution of a long standing problem: Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrödinger equation 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © 2015 by De Gruyter Abstract A long standing problem is completely solved here for the first time. This problem was posed by K. Chadan and P. C. Sabatier in their classical book “Inverse Problems in Quantum Scattering Theory”, Springer, New York, 1977. The inverse scattering problem of the reconstruction of the unknown potential with a compact support in the three-dimensional Schrödinger equation is considered. Only the modulus of the scattering complex-valued wave field is known, whereas the phase is unknown. It is shown that the unknown potential can be reconstructed via the inverse Radon transform. This solution has potential applications in imaging of nanostructures. Romanov, Vladimir G. aut Enthalten in Journal of inverse and ill-posed problems De Gruyter, 1993 23(2015), 4 vom: 21. Mai, Seite 415-428 (DE-627)165676728 (DE-600)1160989-8 (DE-576)04851134X 0928-0219 nnns volume:23 year:2015 number:4 day:21 month:05 pages:415-428 https://doi.org/10.1515/jiip-2015-0025 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_134 GBV_ILN_267 GBV_ILN_4277 AR 23 2015 4 21 05 415-428 |
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10.1515/jiip-2015-0025 doi (DE-627)OLC2138269671 (DE-B1597)jiip-2015-0025-p DE-627 ger DE-627 rakwb 510 VZ 510 VZ 11 ssgn Klibanov, Michael V. verfasserin aut The first solution of a long standing problem: Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrödinger equation 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © 2015 by De Gruyter Abstract A long standing problem is completely solved here for the first time. This problem was posed by K. Chadan and P. C. Sabatier in their classical book “Inverse Problems in Quantum Scattering Theory”, Springer, New York, 1977. The inverse scattering problem of the reconstruction of the unknown potential with a compact support in the three-dimensional Schrödinger equation is considered. Only the modulus of the scattering complex-valued wave field is known, whereas the phase is unknown. It is shown that the unknown potential can be reconstructed via the inverse Radon transform. This solution has potential applications in imaging of nanostructures. Romanov, Vladimir G. aut Enthalten in Journal of inverse and ill-posed problems De Gruyter, 1993 23(2015), 4 vom: 21. Mai, Seite 415-428 (DE-627)165676728 (DE-600)1160989-8 (DE-576)04851134X 0928-0219 nnns volume:23 year:2015 number:4 day:21 month:05 pages:415-428 https://doi.org/10.1515/jiip-2015-0025 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_134 GBV_ILN_267 GBV_ILN_4277 AR 23 2015 4 21 05 415-428 |
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10.1515/jiip-2015-0025 doi (DE-627)OLC2138269671 (DE-B1597)jiip-2015-0025-p DE-627 ger DE-627 rakwb 510 VZ 510 VZ 11 ssgn Klibanov, Michael V. verfasserin aut The first solution of a long standing problem: Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrödinger equation 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © 2015 by De Gruyter Abstract A long standing problem is completely solved here for the first time. This problem was posed by K. Chadan and P. C. Sabatier in their classical book “Inverse Problems in Quantum Scattering Theory”, Springer, New York, 1977. The inverse scattering problem of the reconstruction of the unknown potential with a compact support in the three-dimensional Schrödinger equation is considered. Only the modulus of the scattering complex-valued wave field is known, whereas the phase is unknown. It is shown that the unknown potential can be reconstructed via the inverse Radon transform. This solution has potential applications in imaging of nanostructures. Romanov, Vladimir G. aut Enthalten in Journal of inverse and ill-posed problems De Gruyter, 1993 23(2015), 4 vom: 21. Mai, Seite 415-428 (DE-627)165676728 (DE-600)1160989-8 (DE-576)04851134X 0928-0219 nnns volume:23 year:2015 number:4 day:21 month:05 pages:415-428 https://doi.org/10.1515/jiip-2015-0025 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_134 GBV_ILN_267 GBV_ILN_4277 AR 23 2015 4 21 05 415-428 |
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10.1515/jiip-2015-0025 doi (DE-627)OLC2138269671 (DE-B1597)jiip-2015-0025-p DE-627 ger DE-627 rakwb 510 VZ 510 VZ 11 ssgn Klibanov, Michael V. verfasserin aut The first solution of a long standing problem: Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrödinger equation 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © 2015 by De Gruyter Abstract A long standing problem is completely solved here for the first time. This problem was posed by K. Chadan and P. C. Sabatier in their classical book “Inverse Problems in Quantum Scattering Theory”, Springer, New York, 1977. The inverse scattering problem of the reconstruction of the unknown potential with a compact support in the three-dimensional Schrödinger equation is considered. Only the modulus of the scattering complex-valued wave field is known, whereas the phase is unknown. It is shown that the unknown potential can be reconstructed via the inverse Radon transform. This solution has potential applications in imaging of nanostructures. Romanov, Vladimir G. aut Enthalten in Journal of inverse and ill-posed problems De Gruyter, 1993 23(2015), 4 vom: 21. Mai, Seite 415-428 (DE-627)165676728 (DE-600)1160989-8 (DE-576)04851134X 0928-0219 nnns volume:23 year:2015 number:4 day:21 month:05 pages:415-428 https://doi.org/10.1515/jiip-2015-0025 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_134 GBV_ILN_267 GBV_ILN_4277 AR 23 2015 4 21 05 415-428 |
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10.1515/jiip-2015-0025 doi (DE-627)OLC2138269671 (DE-B1597)jiip-2015-0025-p DE-627 ger DE-627 rakwb 510 VZ 510 VZ 11 ssgn Klibanov, Michael V. verfasserin aut The first solution of a long standing problem: Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrödinger equation 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © 2015 by De Gruyter Abstract A long standing problem is completely solved here for the first time. This problem was posed by K. Chadan and P. C. Sabatier in their classical book “Inverse Problems in Quantum Scattering Theory”, Springer, New York, 1977. The inverse scattering problem of the reconstruction of the unknown potential with a compact support in the three-dimensional Schrödinger equation is considered. Only the modulus of the scattering complex-valued wave field is known, whereas the phase is unknown. It is shown that the unknown potential can be reconstructed via the inverse Radon transform. This solution has potential applications in imaging of nanostructures. Romanov, Vladimir G. aut Enthalten in Journal of inverse and ill-posed problems De Gruyter, 1993 23(2015), 4 vom: 21. Mai, Seite 415-428 (DE-627)165676728 (DE-600)1160989-8 (DE-576)04851134X 0928-0219 nnns volume:23 year:2015 number:4 day:21 month:05 pages:415-428 https://doi.org/10.1515/jiip-2015-0025 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_134 GBV_ILN_267 GBV_ILN_4277 AR 23 2015 4 21 05 415-428 |
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Abstract A long standing problem is completely solved here for the first time. This problem was posed by K. Chadan and P. C. Sabatier in their classical book “Inverse Problems in Quantum Scattering Theory”, Springer, New York, 1977. The inverse scattering problem of the reconstruction of the unknown potential with a compact support in the three-dimensional Schrödinger equation is considered. Only the modulus of the scattering complex-valued wave field is known, whereas the phase is unknown. It is shown that the unknown potential can be reconstructed via the inverse Radon transform. This solution has potential applications in imaging of nanostructures. © 2015 by De Gruyter |
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Abstract A long standing problem is completely solved here for the first time. This problem was posed by K. Chadan and P. C. Sabatier in their classical book “Inverse Problems in Quantum Scattering Theory”, Springer, New York, 1977. The inverse scattering problem of the reconstruction of the unknown potential with a compact support in the three-dimensional Schrödinger equation is considered. Only the modulus of the scattering complex-valued wave field is known, whereas the phase is unknown. It is shown that the unknown potential can be reconstructed via the inverse Radon transform. This solution has potential applications in imaging of nanostructures. © 2015 by De Gruyter |
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Abstract A long standing problem is completely solved here for the first time. This problem was posed by K. Chadan and P. C. Sabatier in their classical book “Inverse Problems in Quantum Scattering Theory”, Springer, New York, 1977. The inverse scattering problem of the reconstruction of the unknown potential with a compact support in the three-dimensional Schrödinger equation is considered. Only the modulus of the scattering complex-valued wave field is known, whereas the phase is unknown. It is shown that the unknown potential can be reconstructed via the inverse Radon transform. This solution has potential applications in imaging of nanostructures. © 2015 by De Gruyter |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2138269671</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230810085946.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230810s2015 xx ||||| 00| ||und c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/jiip-2015-0025</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2138269671</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-B1597)jiip-2015-0025-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">11</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Klibanov, Michael V.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The first solution of a long standing problem: Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrödinger equation</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2015</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© 2015 by De Gruyter</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract A long standing problem is completely solved here for the first time. 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