The position-momentum uncertainty relations for a Pöschl-Teller type potential and its squeezed phenomena

We present the position-momentum uncertainties for the Pöschl-Teller potential. We observe that the Δx decreases with the potential depth λ but increases with quantum number n. Interestingly, we find that the Δp first increases and then decreases with the n. The ΔxΔp first decreases and then increases with the λ, but almost becomes a constant (n+1/2)ℏ for a larger λ. Particularly, there exists a squeezed phenomenon in position x for the lower states. The squeezing in x compensated for by an increase in momentum p, such that ΔxΔp⩾ℏ/2 is still satisfied.