Distributional approach to point interactions in one-dimensional quantum mechanics

We consider the one-dimensional quantum mechanical problem of defining interactions concentrated at a single point in the framework of the theory of distributions. The often ill-defined product which describes the interaction term in the Schrodinger and Dirac equations is replaced by a well-defined...
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Autor*in:	Marcos eCalçada [verfasserIn] José Tadeu Lunardi [verfasserIn] Luiz A. Manzoni [verfasserIn] Wagner eMonteiro [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2014

Schlagwörter:	Distribution Theory Quantum mechanics in one dimension point interactions $delta$-interaction $delta '$-interaction

Übergeordnetes Werk:	In: Frontiers in Physics - Frontiers Media S.A., 2014, 2(2014)
Übergeordnetes Werk:	volume:2 ; year:2014

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3389/fphy.2014.00023

Katalog-ID:	DOAJ009200134

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spelling	10.3389/fphy.2014.00023 doi (DE-627)DOAJ009200134 (DE-599)DOAJa0edaf2d8cd84e97bc3582726d5865ac DE-627 ger DE-627 rakwb eng QC1-999 Marcos eCalçada verfasserin aut Distributional approach to point interactions in one-dimensional quantum mechanics 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We consider the one-dimensional quantum mechanical problem of defining interactions concentrated at a single point in the framework of the theory of distributions. The often ill-defined product which describes the interaction term in the Schrodinger and Dirac equations is replaced by a well-defined distribution satisfying some simple mathematical conditions and, in addition, the physical requirement of probability current conservation is imposed. A four-parameter family of interactions thus emerges as the most general point interaction both in the non-relativistic and in the relativistic theories (in agreement with results obtained by self-adjoint extensions). Since the interaction is given explicitly, the distributional method allows one to carry out symmetry investigations in a simple way, and it proves to be useful to clarify some ambiguities related to the so-called $delta^prime$ interaction. Distribution Theory Quantum mechanics in one dimension point interactions $delta$-interaction $delta '$-interaction Physics José Tadeu Lunardi verfasserin aut Luiz A. Manzoni verfasserin aut Wagner eMonteiro verfasserin aut In Frontiers in Physics Frontiers Media S.A., 2014 2(2014) (DE-627)750371749 (DE-600)2721033-9 2296424X nnns volume:2 year:2014 https://doi.org/10.3389/fphy.2014.00023 kostenfrei https://doaj.org/article/a0edaf2d8cd84e97bc3582726d5865ac kostenfrei http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00023/full kostenfrei https://doaj.org/toc/2296-424X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2 2014
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allfieldsSound	10.3389/fphy.2014.00023 doi (DE-627)DOAJ009200134 (DE-599)DOAJa0edaf2d8cd84e97bc3582726d5865ac DE-627 ger DE-627 rakwb eng QC1-999 Marcos eCalçada verfasserin aut Distributional approach to point interactions in one-dimensional quantum mechanics 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We consider the one-dimensional quantum mechanical problem of defining interactions concentrated at a single point in the framework of the theory of distributions. The often ill-defined product which describes the interaction term in the Schrodinger and Dirac equations is replaced by a well-defined distribution satisfying some simple mathematical conditions and, in addition, the physical requirement of probability current conservation is imposed. A four-parameter family of interactions thus emerges as the most general point interaction both in the non-relativistic and in the relativistic theories (in agreement with results obtained by self-adjoint extensions). Since the interaction is given explicitly, the distributional method allows one to carry out symmetry investigations in a simple way, and it proves to be useful to clarify some ambiguities related to the so-called $delta^prime$ interaction. Distribution Theory Quantum mechanics in one dimension point interactions $delta$-interaction $delta '$-interaction Physics José Tadeu Lunardi verfasserin aut Luiz A. Manzoni verfasserin aut Wagner eMonteiro verfasserin aut In Frontiers in Physics Frontiers Media S.A., 2014 2(2014) (DE-627)750371749 (DE-600)2721033-9 2296424X nnns volume:2 year:2014 https://doi.org/10.3389/fphy.2014.00023 kostenfrei https://doaj.org/article/a0edaf2d8cd84e97bc3582726d5865ac kostenfrei http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00023/full kostenfrei https://doaj.org/toc/2296-424X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2 2014
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topic_facet	Distribution Theory Quantum mechanics in one dimension point interactions $delta$-interaction $delta '$-interaction Physics
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callnumber-first	Q - Science
author	Marcos eCalçada
spellingShingle	Marcos eCalçada misc QC1-999 misc Distribution Theory misc Quantum mechanics in one dimension misc point interactions misc $delta$-interaction misc $delta '$-interaction misc Physics Distributional approach to point interactions in one-dimensional quantum mechanics
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topic_title	QC1-999 Distributional approach to point interactions in one-dimensional quantum mechanics Distribution Theory Quantum mechanics in one dimension point interactions $delta$-interaction $delta '$-interaction
topic	misc QC1-999 misc Distribution Theory misc Quantum mechanics in one dimension misc point interactions misc $delta$-interaction misc $delta '$-interaction misc Physics
topic_unstemmed	misc QC1-999 misc Distribution Theory misc Quantum mechanics in one dimension misc point interactions misc $delta$-interaction misc $delta '$-interaction misc Physics
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title	Distributional approach to point interactions in one-dimensional quantum mechanics
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title_sort	distributional approach to point interactions in one-dimensional quantum mechanics
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title_auth	Distributional approach to point interactions in one-dimensional quantum mechanics
abstract	We consider the one-dimensional quantum mechanical problem of defining interactions concentrated at a single point in the framework of the theory of distributions. The often ill-defined product which describes the interaction term in the Schrodinger and Dirac equations is replaced by a well-defined distribution satisfying some simple mathematical conditions and, in addition, the physical requirement of probability current conservation is imposed. A four-parameter family of interactions thus emerges as the most general point interaction both in the non-relativistic and in the relativistic theories (in agreement with results obtained by self-adjoint extensions). Since the interaction is given explicitly, the distributional method allows one to carry out symmetry investigations in a simple way, and it proves to be useful to clarify some ambiguities related to the so-called $delta^prime$ interaction.
abstractGer	We consider the one-dimensional quantum mechanical problem of defining interactions concentrated at a single point in the framework of the theory of distributions. The often ill-defined product which describes the interaction term in the Schrodinger and Dirac equations is replaced by a well-defined distribution satisfying some simple mathematical conditions and, in addition, the physical requirement of probability current conservation is imposed. A four-parameter family of interactions thus emerges as the most general point interaction both in the non-relativistic and in the relativistic theories (in agreement with results obtained by self-adjoint extensions). Since the interaction is given explicitly, the distributional method allows one to carry out symmetry investigations in a simple way, and it proves to be useful to clarify some ambiguities related to the so-called $delta^prime$ interaction.
abstract_unstemmed	We consider the one-dimensional quantum mechanical problem of defining interactions concentrated at a single point in the framework of the theory of distributions. The often ill-defined product which describes the interaction term in the Schrodinger and Dirac equations is replaced by a well-defined distribution satisfying some simple mathematical conditions and, in addition, the physical requirement of probability current conservation is imposed. A four-parameter family of interactions thus emerges as the most general point interaction both in the non-relativistic and in the relativistic theories (in agreement with results obtained by self-adjoint extensions). Since the interaction is given explicitly, the distributional method allows one to carry out symmetry investigations in a simple way, and it proves to be useful to clarify some ambiguities related to the so-called $delta^prime$ interaction.
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