Information measures of a deformed harmonic oscillator in a static electric field

The Shannon entropy and the Fischer information are calculated for an harmonic oscillator in the presence of an applied electric field (ε) in a space with metrics given by gxx−1∕2=1+γx. For that metric the harmonic oscillator can be mapped into a Morse potential in an Euclidean space. For ε=0, the ground state energy decreases when γ increases. However, for certain values of ε the energy decrease can be canceled out. The dependence of the uncertainties, the entropy, and the information on the parameters γ and ε are shown.