(b) Fisher Information
The fisher information is obtained in terms of the expectation values of the position and momentum wavefunctions. We obtained the analytic expression for the ground state and first excited expectations values as
(22)
(23)
(24)
(25)
(26)
(27)
(28)
where, and are polygamma and Harmonic number respectively.
In table 2, the numerical result of the Fisher information in the ground state and first excited for the various values of is presented. The numerical value features an increasing position space with the corresponding decrease in the momentum. However, their uncertainty relation is satisfied with the SKP for both states. Also, this decreasing and increasing value of Fisher information in the position and momentum spaces respectively is a representation of the location and delocalization of the particle in the system. In table 3, the Heinsberg uncertainty relation is validated for the potential model. The numerical values of show a decreasing trend for both eigenstates and an increasing value for as the value of increases. As the value of decreases, localization increases [23]. For squeezing phenomenon, . With our choice values for , squeezing was seen in for in the momentum space.
Table 2 Numerical results for Fisher information for the ground state and the first excited state