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Classical and Mexican hat-type potential energy curve for the hydrogen molecule from a confined Kratzer oscillator

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Abstract
We review harmonic oscillator theory for closed, stable quantum systems. The H-2 potential energy curve (PEC) of Mexican hat-type, calculated with a confined Kratzer oscillator, is better than the Rydberg-Klein-Rees (RKR) H-2 PEC. Compared with QM, the theory of chemical bonding is simplified, since a confined Kratzer oscillator can also lead to the long sought for universal function, once called the Holy Grail of Molecular Spectroscopy. This is validated by reducing PECs for different bonds H-2, HF, I-2, N-2 and O-2 to a single one. The equal probability for H-2, originating either from H-A + H-B or H-B + H-A, is quantified with a Gauss probability density function. At the Bohr scale, a confined harmonic oscillator behaves properly at the extremes of bound two-nucleon quantum systems.
Keywords
H-2, SYSTEM, ANTIHYDROGEN, Mexican hat curve, quartic harmonic oscillator, hydrogen molecule, Kratzer potential, Universal molecular function, BONDS, MECHANICS, COMMUNICATION, DIATOMIC-MOLECULES, GROUND-STATE, CONSTANTS, MATHEMATICAL-THEORY

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Citation

Please use this url to cite or link to this publication:

Chicago
Van Hooydonk, Guido. 2016. “Classical and Mexican Hat-type Potential Energy Curve for the Hydrogen Molecule from a Confined Kratzer Oscillator.” International Journal of Modern Physics B 30 (9).
APA
Van Hooydonk, G. (2016). Classical and Mexican hat-type potential energy curve for the hydrogen molecule from a confined Kratzer oscillator. INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 30(9).
Vancouver
1.
Van Hooydonk G. Classical and Mexican hat-type potential energy curve for the hydrogen molecule from a confined Kratzer oscillator. INTERNATIONAL JOURNAL OF MODERN PHYSICS B. 2016;30(9).
MLA
Van Hooydonk, Guido. “Classical and Mexican Hat-type Potential Energy Curve for the Hydrogen Molecule from a Confined Kratzer Oscillator.” INTERNATIONAL JOURNAL OF MODERN PHYSICS B 30.9 (2016): n. pag. Print.
@article{8070180,
  abstract     = {We review harmonic oscillator theory for closed, stable quantum systems. The H-2 potential energy curve (PEC) of Mexican hat-type, calculated with a confined Kratzer oscillator, is better than the Rydberg-Klein-Rees (RKR) H-2 PEC. Compared with QM, the theory of chemical bonding is simplified, since a confined Kratzer oscillator can also lead to the long sought for universal function, once called the Holy Grail of Molecular Spectroscopy. This is validated by reducing PECs for different bonds H-2, HF, I-2, N-2 and O-2 to a single one. The equal probability for H-2, originating either from H-A + H-B or H-B + H-A, is quantified with a Gauss probability density function. At the Bohr scale, a confined harmonic oscillator behaves properly at the extremes of bound two-nucleon quantum systems.},
  articleno    = {1650043},
  author       = {Van Hooydonk, Guido},
  issn         = {0217-9792},
  journal      = {INTERNATIONAL JOURNAL OF MODERN PHYSICS B},
  language     = {eng},
  number       = {9},
  pages        = {30},
  title        = {Classical and Mexican hat-type potential energy curve for the hydrogen molecule from a confined Kratzer oscillator},
  url          = {http://dx.doi.org/10.1142/S0217979216500430},
  volume       = {30},
  year         = {2016},
}

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