Exact solutions for shell-confined hydrogen-like atoms: polarisabilities and Shannon entropies.
Saved in:
| Title: | Exact solutions for shell-confined hydrogen-like atoms: polarisabilities and Shannon entropies. |
|---|---|
| Authors: | Burrows, B. L.1 b.l.burrows@staffs.ac.uk, Cohen, M.2 |
| Source: | Molecular Physics. 1/20/2008, Vol. 106 Issue 2-4, p267-273. 7p. 4 Charts, 3 Graphs. |
| Subjects: | Atoms, Polarizability (Electricity), Entropy, Schrödinger equation, Physics |
| Abstract: | An idealised model to treat the effect of spherically confining the electron in a hydrogen-like atom is studied, where the potential is infinite in all space except for a spherical shell. The exact solution of the Schrödinger equation is obtained in terms of two independent solutions of the Kummer equations. It is found that, in some cases, it is necessary to use the standard Kummer M function and a non-standard second solution. In other cases we may use the Kummer U function and in a limiting case the two standard solutions of Bessel's equation. The effect of an imposed dipole field on the shell is treated using the first-order perturbation equation from which the polarisability can be calculated. In addition, the exact wavefunction is used to calculate the Shannon entropies of both position and momentum and it is shown that these measures give insight into the form of the wavefunction. [ABSTRACT FROM AUTHOR] |
| Copyright of Molecular Physics is the property of Taylor & Francis Ltd 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.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 31611708 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Exact solutions for shell-confined hydrogen-like atoms: polarisabilities and Shannon entropies. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Burrows%2C+B%2E+L%2E%22">Burrows, B. L.</searchLink><relatesTo>1</relatesTo><i> b.l.burrows@staffs.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Cohen%2C+M%2E%22">Cohen, M.</searchLink><relatesTo>2</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Molecular+Physics%22">Molecular Physics</searchLink>. 1/20/2008, Vol. 106 Issue 2-4, p267-273. 7p. 4 Charts, 3 Graphs. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Atoms%22">Atoms</searchLink><br /><searchLink fieldCode="DE" term="%22Polarizability+%28Electricity%29%22">Polarizability (Electricity)</searchLink><br /><searchLink fieldCode="DE" term="%22Entropy%22">Entropy</searchLink><br /><searchLink fieldCode="DE" term="%22Schrödinger+equation%22">Schrödinger equation</searchLink><br /><searchLink fieldCode="DE" term="%22Physics%22">Physics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: An idealised model to treat the effect of spherically confining the electron in a hydrogen-like atom is studied, where the potential is infinite in all space except for a spherical shell. The exact solution of the Schrödinger equation is obtained in terms of two independent solutions of the Kummer equations. It is found that, in some cases, it is necessary to use the standard Kummer M function and a non-standard second solution. In other cases we may use the Kummer U function and in a limiting case the two standard solutions of Bessel's equation. The effect of an imposed dipole field on the shell is treated using the first-order perturbation equation from which the polarisability can be calculated. In addition, the exact wavefunction is used to calculate the Shannon entropies of both position and momentum and it is shown that these measures give insight into the form of the wavefunction. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Molecular Physics is the property of Taylor & Francis Ltd 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=31611708 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1080/00268970701787864 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 7 StartPage: 267 Subjects: – SubjectFull: Atoms Type: general – SubjectFull: Polarizability (Electricity) Type: general – SubjectFull: Entropy Type: general – SubjectFull: Schrödinger equation Type: general – SubjectFull: Physics Type: general Titles: – TitleFull: Exact solutions for shell-confined hydrogen-like atoms: polarisabilities and Shannon entropies. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Burrows, B. L. – PersonEntity: Name: NameFull: Cohen, M. IsPartOfRelationships: – BibEntity: Dates: – D: 20 M: 01 Text: 1/20/2008 Type: published Y: 2008 Identifiers: – Type: issn-print Value: 00268976 Numbering: – Type: volume Value: 106 – Type: issue Value: 2-4 Titles: – TitleFull: Molecular Physics Type: main |
| ResultId | 1 |
