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Similarity among quantum-mechanical states: analysis and applications for central potentials.

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Title: Similarity among quantum-mechanical states: analysis and applications for central potentials.
Authors: López-García, I1 (AUTHOR), Angulo, J C1,2 (AUTHOR) angulo@ugr.es, López-Rosa, S2,3 (AUTHOR)
Source: Journal of Physics A: Mathematical & Theoretical. 12/6/2024, Vol. 57 Issue 49, p1-29. 29p.
Subjects: Nuclear charge, Quantum numbers, Quantum states, Hydrogen atom, Statistics
Abstract: The similarity of quantum-mechanical solutions for central potentials is analytically determined and numerically explored for arbitrary dimensionalities. The study here provided focuses on hydrogenic systems and the harmonic oscillator, in respective non-relativistic frameworks. A diversity of analytical expressions for the quantum similarity measure (QSM) and index (QSI) are provided. Relevant conclusions are derived from the analyses grounded on state quantum numbers, space dimensionality and on the role played by the main characteristic parameters of these systems, namely the nuclear charge in the hydrogenic case, and the angular frequency for the oscillator. For this purpose, a statistical analysis of the QSI values has been performed for a large number both of states and combinations of them in each system. Considering the factorization of QSI into a radial and an angular part, particular attention is paid to the individual contribution of each part in both systems. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 181056262
AccessLevel: 6
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  Data: Similarity among quantum-mechanical states: analysis and applications for central potentials.
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  Data: <searchLink fieldCode="AR" term="%22López-García%2C+I%22">López-García, I</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Angulo%2C+J+C%22">Angulo, J C</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> angulo@ugr.es</i><br /><searchLink fieldCode="AR" term="%22López-Rosa%2C+S%22">López-Rosa, S</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Physics+A%3A+Mathematical+%26+Theoretical%22">Journal of Physics A: Mathematical & Theoretical</searchLink>. 12/6/2024, Vol. 57 Issue 49, p1-29. 29p.
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  Data: <searchLink fieldCode="DE" term="%22Nuclear+charge%22">Nuclear charge</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+numbers%22">Quantum numbers</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+states%22">Quantum states</searchLink><br /><searchLink fieldCode="DE" term="%22Hydrogen+atom%22">Hydrogen atom</searchLink><br /><searchLink fieldCode="DE" term="%22Statistics%22">Statistics</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The similarity of quantum-mechanical solutions for central potentials is analytically determined and numerically explored for arbitrary dimensionalities. The study here provided focuses on hydrogenic systems and the harmonic oscillator, in respective non-relativistic frameworks. A diversity of analytical expressions for the quantum similarity measure (QSM) and index (QSI) are provided. Relevant conclusions are derived from the analyses grounded on state quantum numbers, space dimensionality and on the role played by the main characteristic parameters of these systems, namely the nuclear charge in the hydrogenic case, and the angular frequency for the oscillator. For this purpose, a statistical analysis of the QSI values has been performed for a large number both of states and combinations of them in each system. Considering the factorization of QSI into a radial and an angular part, particular attention is paid to the individual contribution of each part in both systems. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Quantum states
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              Text: 12/6/2024
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