![The Pöschl-Teller potential V(x) (in unit of $10^4\;a.u.$) for different parameter values. Dotted line represents the symmetric case ($\rho=\kappa=50$), solid line refers to the slightly asymmetric case ($\rho=50$, $\kappa=46$), while the strongly asymmetric case ($\rho=50$ $\kappa=6$) is shown by the dashed line. Here, the variable $x$ is in atomic units and we have chosen $\alpha=2\;a.u$. []{data-label="potential"}](fig1.eps){width="3.2in"}

Pöschl-Teller potential and the CS wave-packet
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The general PT potential [@posh] is given by $$V(x)\;=\;\frac{\hbar^2\alpha^2}{2m}\left[\frac{\rho(\rho-1)}{\cos^2\alpha x}+\frac{\kappa(\kappa-1)}{\sin^2\alpha x} \right] \label{PT}$$ and it represents an array of potential wells in the whole line. The symmetric case can exhibit energy bands [@ranjani]. Since the wells are impenetrable, it suffices to consider only one of them for a full quantum mechanical description of the system. The potential is depicted in Fig. \[potential\] for different values of $\rho$ and $\kappa$ $(\rho,\kappa>1)$ (units are chosen such that $\hbar=m=1$), and we have selected the well within the interval $[0,\pi/2\alpha]$. The dotted line corresponds to the symmetric well $(\rho=\kappa=50)$, centered around $\pi/4\alpha$. This symmetric well smoothly takes the form of an infinite well in the limit of $\rho,\kappa\rightarrow 1.$ The potential loses its symmetry with respect to the axis of the well if $\rho \neq
\kappa$. Small and large asymmetries are 