Analyzing Generalized Coherent States for Isotropic 3-D Harmonic Oscillator.

Three-dimensional (3-D) harmonic oscillator (HO) coherent states has been constructed for isotropic 3-D case using creation and annihilation operators, extending the analysis of coherent states to systems with spherical symmetry. The quantum characteristics are examined using the wave function Ψ(x, t) where the coherent state's time evolution concludes Gaussian nature of wave packet which keeps the wave packet minimum with time. This configures a non-dispersive Gaussian wave packets over time, maintaining minimal uncertainty and constant energy. We apply the concept of Pauli's non relativistic approximation of spin dependent current to support the derived coherent states for isotropic 3-D HO. Such coherent state is analysed to be association with a spherical symmetric body which is rotating in 3-D plane in such a way that its spin remains perpendicular to its direction of motion keeping total energy constant throughout the motion. This work provides new insights into quantum-classical correspondence, particularly for spherically symmetric quantum systems, and has implications for the design of 3D optical systems and the understanding of polarized light-matter interactions in quantum optics. [ABSTRACT FROM AUTHOR]