Fisher information and Shannon entropy of position-dependent mass oscillators

• Wave functions for position-dependent mass oscillators.
• Fisher information and Shannon entropy for the oscillators.
• Observation of squeezing effect in either position or momentum.

We calculate the Fisher information and the Shannon entropy for three position-dependent mass oscillators. These systems can be seen as deformed harmonic oscillators in the sense that when the deformation parameter (λλ) goes to zero, they are identical to the constant mass harmonic oscillator. For two out of the three oscillators we observe that asλ increases the position Fisher information (FxFx) increases while the momentum Fisher information (FpFp) decreases. On the other hand, the Shannon entropy always increases for the three systems with increasing λλ. Discussion about squeezing effect in either position or momentum due to the λλ variation and a relation between the product of Fisher information and the Shannon entropy are also presented.