Vibration-rotation coupling in a Morse oscillator.
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| Title: | Vibration-rotation coupling in a Morse oscillator. |
|---|---|
| Authors: | Burkhardt, C. E.1, Leventhal, J. J.2 |
| Source: | American Journal of Physics. Aug2007, Vol. 75 Issue 8, p686-689. 4p. |
| Subjects: | Physics, Diatomic molecules, Schrödinger equation, Molecular rotation, Eigenvalues, Vibration (Mechanics), Rotors, Quantum theory |
| Abstract: | The Morse function is invaluable for describing the vibrational motion of diatomic molecules. The time independent Schrodinger equation can be solved in closed form for this potential only if molecular rotation is ignored or if the rotation is isolated from the vibrational motion by approximating it as a rigid rotor. To find the dependence of the energy eigenvalues on the vibrational and rotational state to a level of approximation that includes vibrational-rotational coupling, a higher level of approximation than the rigid rotor model is required. We present a method that can be understood by undergraduates, thus making the Morse potential a more useful example. The method yields results that are identical to those presented by Morse, but in a more elementary way. [ABSTRACT FROM AUTHOR] |
| Copyright of American Journal of Physics is the property of American Institute of Physics 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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| Header | DbId: egs DbLabel: Engineering Source An: 26410815 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Vibration-rotation coupling in a Morse oscillator. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Burkhardt%2C+C%2E+E%2E%22">Burkhardt, C. E.</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Leventhal%2C+J%2E+J%2E%22">Leventhal, J. J.</searchLink><relatesTo>2</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22American+Journal+of+Physics%22">American Journal of Physics</searchLink>. Aug2007, Vol. 75 Issue 8, p686-689. 4p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Physics%22">Physics</searchLink><br /><searchLink fieldCode="DE" term="%22Diatomic+molecules%22">Diatomic molecules</searchLink><br /><searchLink fieldCode="DE" term="%22Schrödinger+equation%22">Schrödinger equation</searchLink><br /><searchLink fieldCode="DE" term="%22Molecular+rotation%22">Molecular rotation</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink><br /><searchLink fieldCode="DE" term="%22Vibration+%28Mechanics%29%22">Vibration (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Rotors%22">Rotors</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+theory%22">Quantum theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The Morse function is invaluable for describing the vibrational motion of diatomic molecules. The time independent Schrodinger equation can be solved in closed form for this potential only if molecular rotation is ignored or if the rotation is isolated from the vibrational motion by approximating it as a rigid rotor. To find the dependence of the energy eigenvalues on the vibrational and rotational state to a level of approximation that includes vibrational-rotational coupling, a higher level of approximation than the rigid rotor model is required. We present a method that can be understood by undergraduates, thus making the Morse potential a more useful example. The method yields results that are identical to those presented by Morse, but in a more elementary way. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of American Journal of Physics is the property of American Institute of Physics 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: 10.1119/1.2750377 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 4 StartPage: 686 Subjects: – SubjectFull: Physics Type: general – SubjectFull: Diatomic molecules Type: general – SubjectFull: Schrödinger equation Type: general – SubjectFull: Molecular rotation Type: general – SubjectFull: Eigenvalues Type: general – SubjectFull: Vibration (Mechanics) Type: general – SubjectFull: Rotors Type: general – SubjectFull: Quantum theory Type: general Titles: – TitleFull: Vibration-rotation coupling in a Morse oscillator. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Burkhardt, C. E. – PersonEntity: Name: NameFull: Leventhal, J. J. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: Aug2007 Type: published Y: 2007 Identifiers: – Type: issn-print Value: 00029505 Numbering: – Type: volume Value: 75 – Type: issue Value: 8 Titles: – TitleFull: American Journal of Physics Type: main |
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