Non-relativistic Oscillator in a Uniform Magnetic Field in Non-commutative Anti-de Sitter Spaces

Abstract

The deformed Schrödinger oscillator in a uniform magnetic field is explicitly calculated in this study using the non-commutative and Anti-de Sitter spaces. The energy eigenvalues are given in their exact forms, and the corresponding radial wave functions are expressed with associated Jacobi polynomials. We determine the critical magnetic field value, which cancels out the normal Zeeman effect. We have also looked into how our system’s thermodynamic properties are affected by the spatial deformation parameters, we remark that the graphs of these quantities show that all thermodynamic quantities, with the exception of the Helmholtz free energy, have an inverse proportion with the deformation parameters \(\theta \) and \(\lambda \). The AdS effect dominates over the NC effect due to its stronger impact on spatial geometry and symmetry.