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

Physics Letters A

One-dimensional harmonic oscillator problem and its hidden SU(1,1) symmetry in the presence of a minimal length

F. A. Dossa

Published Sep 15, 2020• 10 citations
Publisher
DOI
10.1016/j.physleta.2020.126891

Related papers

Quantum SU(1, 1)-harmonic oscillator

Wojciech Mulak

arXiv:hep-th/9312024•Reports on Mathematical Physics•Aug 1, 1993•6 citations

Algebraic Solution of the Harmonic Oscillator With Minimal Length Uncertainty Relations

Kay L. Gemba, Zvonimir Hlousek, Zoltán Papp

In quantum mechanics with minimal length uncertainty relations the Heisenberg-Weyl algebra of the one-dimensional harmonic oscillator is a deformed SU(1,1) algebra. The eigenvalues and eigenstates are constructed algebraically and they form the infinite-dimensional representation of the deformed SU(1,1) algebra. Our construction is independent of prior knowledge of the exact solution of the Schrödinger equation of the model. The approach can be generalized to the $D$-dimensional oscillator with non-commuting coordinates.

arXiv:0712.2078•Dec 13, 2007•2 citations

Hidden symmetries and thermodynamic properties for a harmonic oscillator plus an inverse square potential

Shi‐Hai Dong, Marcelo Lozada‐Cassou, Yu Jiang +2 more

Abstract The exact solutions of a one‐dimensional Schrödinger equation with a harmonic oscillator plus an inverse square potential are obtained. The ladder operators constructed directly from the normalized wavefunctions are found to satisfy a su(1, 1) algebra. Another hidden symmetry is used to explore the relations between the eigenvalues and eigenfunctions by substituting x → −ix. The vibrational partition function Z is calculated exactly to study thermodynamic functions such as the vibrational mean energy U, specific heat C, free energy F, and entropy S. It is both interesting and surprising to find that both vibrational specific heat C and entropy S are independent of the potential strength α. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

International Journal of Quantum Chemistry•Sep 13, 2006•114 citations

SU(1,1) perturbations of the simple harmonic oscillator

A. O. Barut, H Beker, T. Rador

Physics Letters A•Sep 1, 1995•4 citations

1D Quantum Harmonic Oscillator

Brian P. Anderson

SPIE eBooks•Sep 12, 2019•0 citations

Deformed ladder operators for the generalized one- and two-mode squeezed harmonic oscillator in the presence of a minimal length

F. A. Dossa, Gabriel Y. H. Avossevou

We construct the deformed ladder operators in the presence of a minimal length to study the one- and two-mode squeezed harmonic oscillator. The generalized Hamiltonian of the system is expressed in terms of a deformed $$su(1,1)$$ algebra. The realizations of this algebra allow us to convert the purely quantum mechanical problem of the model into a differential equation. By means of the Nikiforov–Uvarov method, the energy eigenvalues are obtained and the corresponding wave functions, in the momentum space, are expressed in terms of hypergeometric functions. Our study shows that the domain of existence of the energy levels is extended and this extension is due to the deformation parameter.

Theoretical and Mathematical Physics•Apr 1, 2022•2 citations
In quantum mechanics with minimal length uncertainty relations the Heisenberg-Weyl algebra of the one-dimensional harmonic oscillator is a deformed SU(1,1) algebra. The eigenvalues and eigenstates are constructed algebraically and they form the infinite-dimensional representation of the deformed SU(1,1) algebra. Our construction is independent of prior knowledge of the exact solution of the Schrödinger equation of the model. The approach can be generalized to the DDD-dimensional oscillator with non-commuting coordinates.
Abstract The exact solutions of a one‐dimensional Schrödinger equation with a harmonic oscillator plus an inverse square potential are obtained. The ladder operators constructed directly from the normalized wavefunctions are found to satisfy a su(1, 1) algebra. Another hidden symmetry is used to explore the relations between the eigenvalues and eigenfunctions by substituting x → −ix. The vibrational partition function Z is calculated exactly to study thermodynamic functions such as the vibrational mean energy U, specific heat C, free energy F, and entropy S. It is both interesting and surprising to find that both vibrational specific heat C and entropy S are independent of the potential strength α. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007
We construct the deformed ladder operators in the presence of a minimal length to study the one- and two-mode squeezed harmonic oscillator. The generalized Hamiltonian of the system is expressed in terms of a deformed su(1,1)su(1,1)su(1,1) algebra. The realizations of this algebra allow us to convert the purely quantum mechanical problem of the model into a differential equation. By means of the Nikiforov–Uvarov method, the energy eigenvalues are obtained and the corresponding wave functions, in the momentum space, are expressed in terms of hypergeometric functions. Our study shows that the domain of existence of the energy levels is extended and this extension is due to the deformation parameter.