Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 093, 9 pages      arXiv:1212.0078      https://doi.org/10.3842/SIGMA.2012.093
Contribution to the Special Issue “Superintegrability, Exact Solvability, and Special Functions”

Coherent States for Tremblay-Turbiner-Winternitz Potential

Yusuf Sucu and Nuri Unal
Department of Physics, Faculty of Science, Akdeniz University, 07058 Antalya, Turkey

Received July 31, 2012, in final form November 28, 2012; Published online December 01, 2012

Abstract
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.

Key words: Tremblay-Turbiner-Winternitz potential; generalized harmonic oscillator; non-central potential; coherent state.

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