Perturbation treatment of local-mode stretching vibrations
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Morse potential
Abstract In this article both notions of Morse decomposition and dynamic Morse decomposition of control systems are studied. The main objective is to present the basic conditions which assure that a Morse decomposition is a dynamic Morse decomposition, and vice-versa. Keywords: control systemasymptotic behaviourMorse decompositionAMS Subject Classifications:: 37N3537B3537B25
Morse potential
Discrete Morse theory
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Morse potential
Harmonic
Simple harmonic motion
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A realization of the ladder operators for the 1D Morse potential is presented. These operators satisfy the SU(2) group. The case of anisotropic 3D Morse potential is also discussed if it can be regarded as three 1D Morse potential. The average values of some observables in the coherent states are also calculated.
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ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTExploring the Morse Potential: MorsePotential.mcdTheresa Julia Zielinski View Author Information Department of Chemistry, Medical Technology, and Physics, Monmouth University, West Long Branch, NJ 07764-1898Cite this: J. Chem. Educ. 1998, 75, 9, 1191Publication Date (Web):September 1, 1998Publication History Received3 August 2009Published online1 September 1998Published inissue 1 September 1998https://pubs.acs.org/doi/10.1021/ed075p1191.1https://doi.org/10.1021/ed075p1191.1research-articleACS PublicationsRequest reuse permissionsArticle Views720Altmetric-Citations1LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose SUBJECTS:Potential energy Get e-Alerts
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Piela replies: The Morse oscillator is a single point mass subject to the Morse original potential cited in Ilya Kaplan’s book, equation 5.22. Contrary to what Donald Truhlar writes, the Morse oscillator does not represent two point masses with a spring, not to mention a diatomic molecule. Therefore, Kaplan’s equation 5.23 is an exact solution of the Schrödinger equation for the Morse oscillator. The same solution is, of course, an approximate one for the Schrödinger equation for two point masses with a Morse-like spring or any real diatomic molecule.Truhlar could literally repeat his arguments for the harmonic oscillator, instead of the Morse one. His conclusion in such a case would mean that the widely known solution to the Schrödinger equation for the harmonic oscillator is not exact. 1 1. L. Piela, Ideas of Quantum Chemistry, Elsevier, Amsterdam (2007), p. 239. REFERENCESSection:ChooseTop of pageREFERENCES <<1. L. Piela, Ideas of Quantum Chemistry, Elsevier, Amsterdam (2007), p. 239. Google Scholar© 2008 American Institute of Physics.
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Simple harmonic motion
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Assuming a symmetric potential and separated self-adjoint boundary conditions, we relate the Maslov and Morse indices for Schr\"odinger operators on $[0, 1]$. We find that the Morse index can be computed in terms of the Maslov index and two associated matrix eigenvalue problems. This provides an efficient way to compute the Morse index for such operators.
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Schrödinger's cat
Matrix (chemical analysis)
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The most commonly used potentials for van der Waals interactions are the Exponential-6 and the Lennard-Jones (12-6) potential. In this paper a correlation between them is described. The Morse function, which is normally applied for quantifying 2-body interactions, has been adopted in one software. This paper deals with the validity of the Morse function for non-bonded interactions by means of obtaining a relationship between the Morse and the Lennard-Jones (12-6) potential functions. An approximate and an exact mathematical relationship is demonstrated to exist between these two potentials.
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Lennard-Jones potential
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Following the attempts by previous authors to construct an effective Morse potential to treat the problem of the Morse potential plus an r−2 term, it is shown that the hypervirial perturbation method, which gives exact results for the Morse potential, also gives results for the perturbed problem which are much more accurate than those of previous authors.
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The recursive method of Requena, Rena, and Zuniga1 for calculating the matrix elements of the Morse oscillator is criticized. The formula is considered not suitable for numerical computations. (AIP)
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Matrix (chemical analysis)
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