The Schrödinger particle on the half-line with an attractive δ-interaction: bound states and resonances
In this paper, we provide a detailed description of the eigenvalue E D ( x 0 ) ≤ 0 (respectively, E N ( x 0 ) ≤ 0 ) of the self-adjoint Hamiltonian operator representing the negative Laplacian on the positive half-line with a Dirichlet (resp. Neuman) boundary condition at the origin perturbed by an...
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| Veröffentlicht in: | European physical journal plus 2021-06, Vol.136 (6), p.673, Article 673 |
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| creator | Fassari, S. Gadella, M. Nieto, L. M. Rinaldi, F. |
| description | In this paper, we provide a detailed description of the eigenvalue
E
D
(
x
0
)
≤
0
(respectively,
E
N
(
x
0
)
≤
0
) of the self-adjoint Hamiltonian operator representing the negative Laplacian on the positive half-line with a Dirichlet (resp. Neuman) boundary condition at the origin perturbed by an attractive Dirac distribution
-
λ
δ
(
x
-
x
0
)
for any fixed value of the magnitude of the coupling constant. We also investigate the
λ
-dependence of both eigenvalues for any fixed value of
x
0
. Furthermore, we show that both systems exhibit resonances as poles of the analytic continuation of the resolvent. These results will be connected with the study of the ground state energy of two remarkable three-dimensional self-adjoint operators, studied in depth in Albeverio’s et al. monograph, perturbed by an attractive
δ
-distribution supported on the spherical shell of radius
r
0
. |
| doi_str_mv | 10.1140/epjp/s13360-021-01636-0 |
| format | Article |
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E
D
(
x
0
)
≤
0
(respectively,
E
N
(
x
0
)
≤
0
) of the self-adjoint Hamiltonian operator representing the negative Laplacian on the positive half-line with a Dirichlet (resp. Neuman) boundary condition at the origin perturbed by an attractive Dirac distribution
-
λ
δ
(
x
-
x
0
)
for any fixed value of the magnitude of the coupling constant. We also investigate the
λ
-dependence of both eigenvalues for any fixed value of
x
0
. Furthermore, we show that both systems exhibit resonances as poles of the analytic continuation of the resolvent. These results will be connected with the study of the ground state energy of two remarkable three-dimensional self-adjoint operators, studied in depth in Albeverio’s et al. monograph, perturbed by an attractive
δ
-distribution supported on the spherical shell of radius
r
0
.</description><identifier>ISSN: 2190-5444</identifier><identifier>EISSN: 2190-5444</identifier><identifier>DOI: 10.1140/epjp/s13360-021-01636-0</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applied and Technical Physics ; Atomic ; Boundary conditions ; Complex Systems ; Condensed Matter Physics ; Dirichlet problem ; Eigenvalues ; Mathematical and Computational Physics ; Mathematical functions ; Molecular ; Optical and Plasma Physics ; Physics ; Physics and Astronomy ; Quantum dots ; Quantum field theory ; Quantum physics ; Regular Article ; Spherical shells ; Theoretical</subject><ispartof>European physical journal plus, 2021-06, Vol.136 (6), p.673, Article 673</ispartof><rights>The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021</rights><rights>The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c334t-f8ed47015644d891b68bde21d6a993f34b595f3fc995cbdc9a796e17948e79e63</citedby><cites>FETCH-LOGICAL-c334t-f8ed47015644d891b68bde21d6a993f34b595f3fc995cbdc9a796e17948e79e63</cites><orcidid>0000-0003-3475-7696 ; 0000-0002-0087-3042 ; 0000-0002-2849-2647 ; 0000-0001-8860-990X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1140/epjp/s13360-021-01636-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2920358037?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,21388,27924,27925,33744,41488,42557,43805,51319,64385,64389,72469</link.rule.ids></links><search><creatorcontrib>Fassari, S.</creatorcontrib><creatorcontrib>Gadella, M.</creatorcontrib><creatorcontrib>Nieto, L. M.</creatorcontrib><creatorcontrib>Rinaldi, F.</creatorcontrib><title>The Schrödinger particle on the half-line with an attractive δ-interaction: bound states and resonances</title><title>European physical journal plus</title><addtitle>Eur. Phys. J. Plus</addtitle><description>In this paper, we provide a detailed description of the eigenvalue
E
D
(
x
0
)
≤
0
(respectively,
E
N
(
x
0
)
≤
0
) of the self-adjoint Hamiltonian operator representing the negative Laplacian on the positive half-line with a Dirichlet (resp. Neuman) boundary condition at the origin perturbed by an attractive Dirac distribution
-
λ
δ
(
x
-
x
0
)
for any fixed value of the magnitude of the coupling constant. We also investigate the
λ
-dependence of both eigenvalues for any fixed value of
x
0
. Furthermore, we show that both systems exhibit resonances as poles of the analytic continuation of the resolvent. These results will be connected with the study of the ground state energy of two remarkable three-dimensional self-adjoint operators, studied in depth in Albeverio’s et al. monograph, perturbed by an attractive
δ
-distribution supported on the spherical shell of radius
r
0
.</description><subject>Applied and Technical Physics</subject><subject>Atomic</subject><subject>Boundary conditions</subject><subject>Complex Systems</subject><subject>Condensed Matter Physics</subject><subject>Dirichlet problem</subject><subject>Eigenvalues</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical functions</subject><subject>Molecular</subject><subject>Optical and Plasma Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum dots</subject><subject>Quantum field theory</subject><subject>Quantum physics</subject><subject>Regular Article</subject><subject>Spherical shells</subject><subject>Theoretical</subject><issn>2190-5444</issn><issn>2190-5444</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqFkM9KxDAQxosouKz7DAY8R5MmTRtvsvgPFjy4nkOaTG2WNa1JVvG9xBfw7jPZ3Qp6cy4zw3zfN_DLsmNKTinl5Az6VX8WKWOCYJJTTKhgApO9bJJTSXDBOd__Mx9msxhXZCguKZd8krllC-jetOHzwzr_CAH1OiRn1oA6j9JwbPW6wWvnAb261CLtkU4paJPcC6Cvd-x8gt3a-XNUdxtvUUw6QRykFgWIndfeQDzKDhq9jjD76dPs4epyOb_Bi7vr2_nFAhvGeMJNBZaXhBaCc1tJWouqtpBTK7SUrGG8LmTRsMZIWZjaGqlLKYCWkldQShBsmp2MuX3onjcQk1p1m-CHlyqXOWFFRVg5qMpRZUIXY4BG9cE96fCmKFFbtGqLVo1o1YBW7dAqMjir0RkHx5bYb_5_1m-LRIIG</recordid><startdate>20210601</startdate><enddate>20210601</enddate><creator>Fassari, S.</creator><creator>Gadella, M.</creator><creator>Nieto, L. M.</creator><creator>Rinaldi, F.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>BKSAR</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>P5Z</scope><scope>P62</scope><scope>PCBAR</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><orcidid>https://orcid.org/0000-0003-3475-7696</orcidid><orcidid>https://orcid.org/0000-0002-0087-3042</orcidid><orcidid>https://orcid.org/0000-0002-2849-2647</orcidid><orcidid>https://orcid.org/0000-0001-8860-990X</orcidid></search><sort><creationdate>20210601</creationdate><title>The Schrödinger particle on the half-line with an attractive δ-interaction: bound states and resonances</title><author>Fassari, S. ; Gadella, M. ; Nieto, L. M. ; Rinaldi, F.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c334t-f8ed47015644d891b68bde21d6a993f34b595f3fc995cbdc9a796e17948e79e63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Applied and Technical Physics</topic><topic>Atomic</topic><topic>Boundary conditions</topic><topic>Complex Systems</topic><topic>Condensed Matter Physics</topic><topic>Dirichlet problem</topic><topic>Eigenvalues</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical functions</topic><topic>Molecular</topic><topic>Optical and Plasma Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum dots</topic><topic>Quantum field theory</topic><topic>Quantum physics</topic><topic>Regular Article</topic><topic>Spherical shells</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fassari, S.</creatorcontrib><creatorcontrib>Gadella, M.</creatorcontrib><creatorcontrib>Nieto, L. M.</creatorcontrib><creatorcontrib>Rinaldi, F.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>Earth, Atmospheric & Aquatic Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Earth, Atmospheric & Aquatic Science Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><jtitle>European physical journal plus</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fassari, S.</au><au>Gadella, M.</au><au>Nieto, L. M.</au><au>Rinaldi, F.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Schrödinger particle on the half-line with an attractive δ-interaction: bound states and resonances</atitle><jtitle>European physical journal plus</jtitle><stitle>Eur. Phys. J. Plus</stitle><date>2021-06-01</date><risdate>2021</risdate><volume>136</volume><issue>6</issue><spage>673</spage><pages>673-</pages><artnum>673</artnum><issn>2190-5444</issn><eissn>2190-5444</eissn><abstract>In this paper, we provide a detailed description of the eigenvalue
E
D
(
x
0
)
≤
0
(respectively,
E
N
(
x
0
)
≤
0
) of the self-adjoint Hamiltonian operator representing the negative Laplacian on the positive half-line with a Dirichlet (resp. Neuman) boundary condition at the origin perturbed by an attractive Dirac distribution
-
λ
δ
(
x
-
x
0
)
for any fixed value of the magnitude of the coupling constant. We also investigate the
λ
-dependence of both eigenvalues for any fixed value of
x
0
. Furthermore, we show that both systems exhibit resonances as poles of the analytic continuation of the resolvent. These results will be connected with the study of the ground state energy of two remarkable three-dimensional self-adjoint operators, studied in depth in Albeverio’s et al. monograph, perturbed by an attractive
δ
-distribution supported on the spherical shell of radius
r
0
.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1140/epjp/s13360-021-01636-0</doi><orcidid>https://orcid.org/0000-0003-3475-7696</orcidid><orcidid>https://orcid.org/0000-0002-0087-3042</orcidid><orcidid>https://orcid.org/0000-0002-2849-2647</orcidid><orcidid>https://orcid.org/0000-0001-8860-990X</orcidid></addata></record> |
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| ispartof | European physical journal plus, 2021-06, Vol.136 (6), p.673, Article 673 |
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| language | eng |
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| subjects | Applied and Technical Physics Atomic Boundary conditions Complex Systems Condensed Matter Physics Dirichlet problem Eigenvalues Mathematical and Computational Physics Mathematical functions Molecular Optical and Plasma Physics Physics Physics and Astronomy Quantum dots Quantum field theory Quantum physics Regular Article Spherical shells Theoretical |
| title | The Schrödinger particle on the half-line with an attractive δ-interaction: bound states and resonances |
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