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On a class of anharmonic oscillators

Marianna Chatzakou (UGent) , Julio Delgado and Michael Ruzhansky (UGent)
(2021) JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES. 153. p.1-29
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Abstract
In this work, we study a class of anharmonic oscillators within the framework of the Weyl-Hörmander calculus. We obtain spectral properties in terms of Schatten-von Neumann classes for their negative powers and derive from them estimates on the rate of growth for the eigenvalues of the anharmonic oscillator. In particular, we give a simple proof for the main term of the spectral asymptotics of these operators. We also study some examples of anharmonic oscillators arising from the analysis on Lie groups.
Keywords
Anharmonic oscillators, Schrödinger equation, Energy levels, Nonhomogeneous calculus, Microlocal analysis, Growth of eigenvalues, NONCOMMUTATIVE HARMONIC-OSCILLATORS, VON-NEUMANN PROPERTIES, PSEUDODIFFERENTIAL-OPERATORS, SCHATTEN CLASSES, WEYL CALCULUS, SPECTRUM, TRACES, SPACES

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MLA
Chatzakou, Marianna, et al. “On a Class of Anharmonic Oscillators.” JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, vol. 153, 2021, pp. 1–29, doi:10.1016/j.matpur.2021.07.006.
APA
Chatzakou, M., Delgado, J., & Ruzhansky, M. (2021). On a class of anharmonic oscillators. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 153, 1–29. https://doi.org/10.1016/j.matpur.2021.07.006
Chicago author-date
Chatzakou, Marianna, Julio Delgado, and Michael Ruzhansky. 2021. “On a Class of Anharmonic Oscillators.” JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES 153: 1–29. https://doi.org/10.1016/j.matpur.2021.07.006.
Chicago author-date (all authors)
Chatzakou, Marianna, Julio Delgado, and Michael Ruzhansky. 2021. “On a Class of Anharmonic Oscillators.” JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES 153: 1–29. doi:10.1016/j.matpur.2021.07.006.
Vancouver
1.
Chatzakou M, Delgado J, Ruzhansky M. On a class of anharmonic oscillators. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES. 2021;153:1–29.
IEEE
[1]
M. Chatzakou, J. Delgado, and M. Ruzhansky, “On a class of anharmonic oscillators,” JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, vol. 153, pp. 1–29, 2021.
@article{8754755,
  abstract     = {{In this work, we study a class of anharmonic oscillators within the framework of the Weyl-Hörmander calculus. We obtain spectral properties in terms of Schatten-von Neumann classes for their negative powers and derive from them estimates on the rate of growth for the eigenvalues of the anharmonic oscillator. In particular, we give a simple proof for the main term of the spectral asymptotics of these operators. We also study some examples of anharmonic oscillators arising from the analysis on Lie groups.}},
  author       = {{Chatzakou, Marianna and Delgado, Julio and Ruzhansky, Michael}},
  issn         = {{0021-7824}},
  journal      = {{JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES}},
  keywords     = {{Anharmonic oscillators,Schrödinger equation,Energy levels,Nonhomogeneous calculus,Microlocal analysis,Growth of eigenvalues,NONCOMMUTATIVE HARMONIC-OSCILLATORS,VON-NEUMANN PROPERTIES,PSEUDODIFFERENTIAL-OPERATORS,SCHATTEN CLASSES,WEYL CALCULUS,SPECTRUM,TRACES,SPACES}},
  language     = {{eng}},
  pages        = {{1--29}},
  title        = {{On a class of anharmonic oscillators}},
  url          = {{http://doi.org/10.1016/j.matpur.2021.07.006}},
  volume       = {{153}},
  year         = {{2021}},
}
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