Quasi exact solutions for an asymmetric double well potential.
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| Title: | Quasi exact solutions for an asymmetric double well potential. |
|---|---|
| Authors: | Burrows, B. L., Cohen, M., Feldmann, Tova |
| Source: | Molecular Physics. 6/20/96, Vol. 88 Issue 3, p611-620. 10p. |
| Subjects: | Quantum wells, Potential theory (Physics) |
| Abstract: | Algebraic methods are used to derive approximate quasi exact solutions for a parametric model potential having the functional form V(x) = V0 - Mbetax + 1/2x2(alpha + betax)2 with M a positive integer and beta > 0. This yields an asymmetric double well potential provided that the parameters (M, alpha, beta) satisfy the conditions -1/12 3 < omega = - Mbeta2/2alpha3 < 1/12 3. If k = alpha2/beta is sufficiently large there is a high barrier between the two wells, and the quasi exact spectrum is essentially harmonic. More generally, each quasi exact solution is the product of a finite polynomial and a universal asymptotic factor, exp[-(1/2alphax2 + 1/3betax3)], and is mainly localized in the deeper well, even when the spectrum is significantly non-harmonic. For omega sufficiently small, both the quasi exact spectrum and the lower excited bound state spectrum are determined quite accurately by low order Rayleigh-Schrodinger perturbation theory following a suitable (but non-standard) canonical transformation of the reduced Hamiltonian. [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 |
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| Items | – Name: Title Label: Title Group: Ti Data: Quasi exact solutions for an asymmetric double well potential. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Burrows%2C+B%2E+L%2E%22">Burrows, B. L.</searchLink><br /><searchLink fieldCode="AR" term="%22Cohen%2C+M%2E%22">Cohen, M.</searchLink><br /><searchLink fieldCode="AR" term="%22Feldmann%2C+Tova%22">Feldmann, Tova</searchLink> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Molecular+Physics%22">Molecular Physics</searchLink>. 6/20/96, Vol. 88 Issue 3, p611-620. 10p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Quantum+wells%22">Quantum wells</searchLink><br /><searchLink fieldCode="DE" term="%22Potential+theory+%28Physics%29%22">Potential theory (Physics)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Algebraic methods are used to derive approximate quasi exact solutions for a parametric model potential having the functional form V(x) = V0 - Mbetax + 1/2x2(alpha + betax)2 with M a positive integer and beta > 0. This yields an asymmetric double well potential provided that the parameters (M, alpha, beta) satisfy the conditions -1/12 3 < omega = - Mbeta2/2alpha3 < 1/12 3. If k = alpha2/beta is sufficiently large there is a high barrier between the two wells, and the quasi exact spectrum is essentially harmonic. More generally, each quasi exact solution is the product of a finite polynomial and a universal asymptotic factor, exp[-(1/2alphax2 + 1/3betax3)], and is mainly localized in the deeper well, even when the spectrum is significantly non-harmonic. For omega sufficiently small, both the quasi exact spectrum and the lower excited bound state spectrum are determined quite accurately by low order Rayleigh-Schrodinger perturbation theory following a suitable (but non-standard) canonical transformation of the reduced Hamiltonian. [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.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1080/00268979609482441 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 10 StartPage: 611 Subjects: – SubjectFull: Quantum wells Type: general – SubjectFull: Potential theory (Physics) Type: general Titles: – TitleFull: Quasi exact solutions for an asymmetric double well potential. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Burrows, B. L. – PersonEntity: Name: NameFull: Cohen, M. – PersonEntity: Name: NameFull: Feldmann, Tova IsPartOfRelationships: – BibEntity: Dates: – D: 20 M: 06 Text: 6/20/96 Type: published Y: 1996 Identifiers: – Type: issn-print Value: 00268976 Numbering: – Type: volume Value: 88 – Type: issue Value: 3 Titles: – TitleFull: Molecular Physics Type: main |
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