Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

From harmonic to anharmonic oscillators

FRANCESCO IACHELLO

Published Jan 1, 1993• 0 citations
OpenAlex

Abstract

The algebraic approach to quantum mechanics is briefly reviewed. The role of oscillator realizations is discussed. Applications to vibrations of complex molecules are presented.

Related papers

The Harmonic Oscillator, a Review of Classicaland Elementary Quantum Mechanics

Carl W David

The classical harmonic oscillator and an elementary discussion of the quantum mechanical solutions for the harmonic oscillator are discussed.

•Jan 1, 2006•0 citations

Coupled Q-oscillators as a model for vibrations of polyatomic molecules

Dennis Bonatsos A, Daskaloyannis, C, Kolokotronis, P

The system of two $Q$-deformed oscillators coupled so that the total Hamiltonian has the su$_Q$(2) symmetry is proved to be equivalent, to lowest order approximation, to a system of two identical Morse oscillators coupled by the cross-anharmonicity usually used empirically in describing vibrational spectra of triatomic molecules. The symmetry also imposes a connection between the self-anharmonicity of the Morse oscillators and the cross-anharmonicity strength, which can be removed by replacing the $Q$-oscillators by deformed anharmonic oscillators. The generalization to $n$ oscillators is straightforward. The applicability of the formalism to highly symmetric polyatomic molecules is discussed.

•Jan 1, 1996•21 citations

Coupled Q-oscillators as a model for vibrations of polyatomic molecules

Dennis Bonatsos, C. Daskaloyannis, P. Kolokotronis

The system of two Q-deformed oscillators coupled so that the total Hamiltonian has the suQ(2) symmetry is proved to be equivalent, to lowest order approximation, to a system of two identical Morse oscillators coupled by the cross-anharmonicity usually used empirically in describing vibrational spectra of triatomic molecules. The symmetry also imposes a connection between the self-anharmonicity of the Morse oscillators and the cross-anharmonicity strength, which can be removed by replacing the Q-oscillators by deformed anharmonic oscillators. The generalization to n oscillators is straightforward. The applicability of the formalism to highly symmetric polyatomic molecules is discussed.

arXiv:quant-ph/9701025•The Journal of Chemical Physics•Jan 8, 1997•30 citations

The Harmonic Oscillator

Steven A. Adelman

In Chapters 2 and 4 – 6 , we developed the mathematical and physical foundations of quantum mechanics. In this and the remaining chapters, we describe successively advanced applications of these foundations.

CRC Press eBooks•May 31, 2021•0 citations

Molecules and the Eigenstate Thermalization Hypothesis

David M. Leitner

We review a theory that predicts the onset of thermalization in a quantum mechanical coupled non-linear oscillator system, which models the vibrational degrees of freedom of a molecule. A system of N non-linear oscillators perturbed by cubic anharmonic interactions exhibits a many-body localization (MBL) transition in the vibrational state space (VSS) of the molecule. This transition can occur at rather high energy in a sizable molecule because the density of states coupled by cubic anharmonic terms scales as N3, in marked contrast to the total density of states, which scales as exp(aN), where a is a constant. The emergence of a MBL transition in the VSS is seen by analysis of a random matrix ensemble that captures the locality of coupling in the VSS, referred to as local random matrix theory (LRMT). Upon introducing higher order anharmonicity, the location of the MBL transition of even a sizable molecule, such as an organic molecule with tens of atoms, still lies at an energy that may exceed the energy to surmount a barrier to reaction, such as a barrier to conformational change. Illustrative calculations are provided, and some recent work on the influence of thermalization on thermal conduction in molecular junctions is also discussed.

Entropy•Sep 5, 2018•16 citations

Quantum theory of anharmonic oscillators: Energy levels of a single and a pair of coupled oscillators with quartic coupling

F. T. Hioe, D. B. Macmillen, Elliot W. Montroll

Physics Reports•Jul 1, 1978•246 citations
The system of two QQQ-deformed oscillators coupled so that the total Hamiltonian has the suQ_QQ​(2) symmetry is proved to be equivalent, to lowest order approximation, to a system of two identical Morse oscillators coupled by the cross-anharmonicity usually used empirically in describing vibrational spectra of triatomic molecules. The symmetry also imposes a connection between the self-anharmonicity of the Morse oscillators and the cross-anharmonicity strength, which can be removed by replacing the QQQ-oscillators by deformed anharmonic oscillators. The generalization to nnn oscillators is straightforward. The applicability of the formalism to highly symmetric polyatomic molecules is discussed.
The system of two Q-deformed oscillators coupled so that the total Hamiltonian has the suQ(2) symmetry is proved to be equivalent, to lowest order approximation, to a system of two identical Morse oscillators coupled by the cross-anharmonicity usually used empirically in describing vibrational spectra of triatomic molecules. The symmetry also imposes a connection between the self-anharmonicity of the Morse oscillators and the cross-anharmonicity strength, which can be removed by replacing the Q-oscillators by deformed anharmonic oscillators. The generalization to n oscillators is straightforward. The applicability of the formalism to highly symmetric polyatomic molecules is discussed.
We review a theory that predicts the onset of thermalization in a quantum mechanical coupled non-linear oscillator system, which models the vibrational degrees of freedom of a molecule. A system of N non-linear oscillators perturbed by cubic anharmonic interactions exhibits a many-body localization (MBL) transition in the vibrational state space (VSS) of the molecule. This transition can occur at rather high energy in a sizable molecule because the density of states coupled by cubic anharmonic terms scales as N3, in marked contrast to the total density of states, which scales as exp(aN), where a is a constant. The emergence of a MBL transition in the VSS is seen by analysis of a random matrix ensemble that captures the locality of coupling in the VSS, referred to as local random matrix theory (LRMT). Upon introducing higher order anharmonicity, the location of the MBL transition of even a sizable molecule, such as an organic molecule with tens of atoms, still lies at an energy that may exceed the energy to surmount a barrier to reaction, such as a barrier to conformational change. Illustrative calculations are provided, and some recent work on the influence of thermalization on thermal conduction in molecular junctions is also discussed.