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

Open Physics

Coherent states for Smorodinsky-Winternitz potentials

Nuri Ünal

Published Apr 17, 2009• 7 citations
Publisher

Abstract

Abstract In this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional harmonic oscillator problem. In the first case, we find the non-spreading wave packets by transforming the system into four oscillators in Cartesian, and also polar, coordinates. In the second case, the coherent states are constructed in Cartesian coordinates by transforming the system into three non-isotropic harmonic oscillators. All of these states evolve in physical-time. We also show that in parametric-time, the second case can be transformed to the first one with vanishing eigenvalues.

DOI
10.2478/s11534-009-0039-3

Related papers

Smorodinsky-Winternitz potentials: Coherent state approach

Nuri Ünal

In this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional harmonic oscillator problem and the Kepler-Coulomb problem. In the first case we find the nonspreading wave packets by transforming the system into four oscillators in Cartesian, and also polar, coordinates. In the second case, the coherent states are constructed in Cartesian coordinates by transforming the system into three nonisotropic harmonic oscillators. All of these states evolve in physical-time. In the third case, the system is transformed into four oscillators and the parametric-time coherent states are constructed in two coordinate frames. In the fourth case, the system is transformed into two oscillators with the reflection symmetry and the parametrictime coherent states are constructed in two coordinate frames.

Physics of Atomic Nuclei•Dec 1, 2011•2 citations

Parametric-time coherent states for Smorodinsky-Winternitz potentials

Nuri Ünal

In this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional Kepler problem. In the third case, the system is transformed into four ocillators and the parametric-time coherent states are constructed in two coordinate frames. In the fourth case, the system is transformed into two ocillators with the reflection symmetry and the parametric-time coherent states are constructed in two coordinate frames.

Journal of Mathematical Physics•Dec 1, 2007•7 citations

D-dimensional Smorodinsky-Winternitz potential: Coherent state approach

Nuri Ünal

In this study, we construct the coherent states for a particle in the D -dimensional maximally superintegrable Smorodinsky-Winternitz potential. We, first, map the system into 2 D harmonic oscillators, second, construct the coherent states of them by evaluating the transition amplitudes. Third, in the Cartesian and the hyperspherical coordinates, we find the coherent states and the stationary states of the original sytem by reduction.

Physics of Atomic Nuclei•Oct 1, 2013•0 citations

Coherent States for Tremblay-Turbiner-Winternitz Potential

Yusuf Sucu

In this study, we construct the coherent states for a particle in the Tremblay-Turbiner-Winternitz potential by finding the conserved charge coherent states of the four harmonic oscillators in the polar coordinates.We also derive the energy eigenstates of the potential and show that the center of the coherent states follow the classical orbits of the particle.

arXiv:1212.0078•Symmetry Integrability and Geometry Methods and Applications•Dec 1, 2012•0 citations

Coherent states for Kratzer-type potentials

Nalan Kandırmaz

The coherent states for a particle in Kratzer type potentials are constructed by solving Feynman’s path integral. The action of the generalized Kratzer potential is transformed into two harmonic oscillators by Levi-Civita transformation to derive the parametric time coherent states. Green’s function, energy eigenvalues, and the corresponding wave functions for this potential are calculated. The evaluated results are reduced to the modified Kratzer potentials and Kratzer-Fues oscillators which are special cases of the generalized Kratzer potential.

Journal of Mathematical Physics•Jun 1, 2018•6 citations

Radial coherent states for central potentials: The isotropic harmonic oscillator

Christopher C. Gerry, Jerry Kiefer

We formulate radial coherent states for the isotropic harmonic oscillator from the unitary irreducible representations associated with the radial spectrum-generating group Sp(2) which is locally isomorphic to SU(1,1) and SO(2,1). We further consider the time evolution of a coherent-state wave packet and show that, in contrast to the ordinary oscillator coherent states, this wave packet does change its shape (periodically) as it evolves. This change of shape may be interpreted in terms of a generalized squeezing.

Physical Review A•Jul 1, 1988•15 citations
Abstract In this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional harmonic oscillator problem. In the first case, we find the non-spreading wave packets by transforming the system into four oscillators in Cartesian, and also polar, coordinates. In the second case, the coherent states are constructed in Cartesian coordinates by transforming the system into three non-isotropic harmonic oscillators. All of these states evolve in physical-time. We also show that in parametric-time, the second case can be transformed to the first one with vanishing eigenvalues.
In this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional harmonic oscillator problem and the Kepler-Coulomb problem. In the first case we find the nonspreading wave packets by transforming the system into four oscillators in Cartesian, and also polar, coordinates. In the second case, the coherent states are constructed in Cartesian coordinates by transforming the system into three nonisotropic harmonic oscillators. All of these states evolve in physical-time. In the third case, the system is transformed into four oscillators and the parametric-time coherent states are constructed in two coordinate frames. In the fourth case, the system is transformed into two oscillators with the reflection symmetry and the parametrictime coherent states are constructed in two coordinate frames.
The coherent states for a particle in Kratzer type potentials are constructed by solving Feynman’s path integral. The action of the generalized Kratzer potential is transformed into two harmonic oscillators by Levi-Civita transformation to derive the parametric time coherent states. Green’s function, energy eigenvalues, and the corresponding wave functions for this potential are calculated. The evaluated results are reduced to the modified Kratzer potentials and Kratzer-Fues oscillators which are special cases of the generalized Kratzer potential.
We formulate radial coherent states for the isotropic harmonic oscillator from the unitary irreducible representations associated with the radial spectrum-generating group Sp(2) which is locally isomorphic to SU(1,1) and SO(2,1). We further consider the time evolution of a coherent-state wave packet and show that, in contrast to the ordinary oscillator coherent states, this wave packet does change its shape (periodically) as it evolves. This change of shape may be interpreted in terms of a generalized squeezing.