# Coherent States for Tremblay{Turbiner{Winternitz Potential ?

@article{Sucu2012CoherentSF,
title={Coherent States for Tremblay\{Turbiner\{Winternitz Potential ?},
author={Yusuf Sucu and Nuri Unal},
journal={Symmetry Integrability and Geometry-methods and Applications},
year={2012},
volume={8},
pages={093}
}
• Published 1 December 2012
• Physics
• Symmetry Integrability and Geometry-methods and Applications
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.

## References

SHOWING 1-10 OF 26 REFERENCES
Coherent states for Smorodinsky-Winternitz potentials
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
Parametric-time coherent states for Smorodinsky-Winternitz potentials
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
Parametric time-coherent states for the hydrogen atom
We obtained coherent states for the hydrogen atom by transforming the problem into four oscillators in the parametric time at a classical level, and quantizing these oscillators by using path
Parametric-time coherent states for the generalized MIC-Kepler system
In this study, we construct the parametric-time coherent states for the negative energy states of the generalized MIC-Kepler system, in which a charged particle is in a monopole vector potential, a
Parametric-time coherent states for Morse potential
We transform the Lagrangian of the Morse-potential problem into two harmonic oscillators in a new parametric time and quantize this system by using path integrals over holomorphic coordinates of
Group theory of the Smorodinsky-Winternitz system
The three degrees of freedom Smorodinsky–Winternitz system is a degenerate or super‐integrable Hamiltonian that possesses five functionally independent globally defined and single‐valued integrals of
Superintegrability and higher-order constants for classical and quantum systems
• Mathematics
• 2011
We extend recent work by Tremblay, Turbiner, and Winternitz which analyzes an infinite family of solvable and integrable quantum systems in the plane, indexed by the positive parameter k. Key
Superintegrability of the Tremblay-Turbiner-Winternitz quantum Hamiltonians on a plane for odd $k$
In a recent FTC by Tremblay {\sl et al} (2009 {\sl J. Phys. A: Math. Theor.} {\bf 42} 205206), it has been conjectured that for any integer value of $k$, some novel exactly solvable and integrable
A Treatise on the Theory of Bessel Functions
THE memoir in which Bessel, the astronomer, examined in detail the functions which now bear his name was published in 1824, and was the outcome of his earlier researches concerning the expression of
Quasi-coherent states for harmonic oscillator with time-dependent parameters
In this study, we discuss the harmonic oscillator with the time-dependent frequency, ω(t), and the mass, M(t), by generalizing the holomorphic coordinates for the harmonic oscillator. In general