Information theoretic measures of uncertainty of a noncommutative anisotropic oscillator in a homogeneous magnetic field

Abstract

A noncommutative anisotropic oscillator in the presence of a homogeneous magnetic field is studied and the Schrödinger equation is solved analytically. We evaluated various information theoretic measures of uncertainty e.g., Heisenberg uncertainty relation, Shannon area and Fisher area for several states, including the ground state. It has been shown that the ground state is coherent for different magnetic fields. The optimum values of the Shannon area have found in position and momentum spaces. We observe that the Fisher area in momentum space has a maximum value without a magnetic field. Bialynicki–Birula–Mycielski (BBM) and Cramer–Rao uncertainty relations have been verified.