Information theory and thermodynamic study of a 2D harmonic oscillator modified by inverse-square potential

This work provides analytical study of a two-dimensional quantum harmonic oscillator (HO) coupled with a perpendicular magnetic field (B) in the x-direction and an inverse-square potential in the y-direction. The system’s Hamiltonian is exactly solved via variable separation, to obtain the energy levels and wavefunctions composed of Hermite and associated Laguerre polynomials. Fisher information (FI) and Shannon entropy (SE) for both position space (PS) and momentum space (MS) are fully examined under the magnetic field strength and anisotropic potential parameters. The canonical partition function is computed and thermodynamic quantities such as internal energy, entropy, and Gibbs free energy are evaluated. The result shows that the presence of magnetic field enhances spatial localization and reduces uncertainty in PS but has a revised effect in the MS. In the thermodynamic properties, there is asymmetric thermodynamic responses in the x- and y-directions due to the presence of the magnetic field and the inverse-square potential. This study highlights the deep relationship between quantum information theory and thermodynamics in low-dimensional systems with structured interactions.