QM-22 WKB Approximation

A few potentials are drawn in figure below. The turning points are marked as  open circles for energies indicated by  dashed horizontal lines.

                                                  Fig 1 Potentials with two turnung points

 For potential in Fig 1 (a), there are two turning points for all energies. The potential in \Fig1(b) has two turning points for some energies and  four  turning points for some other energies. Fig  below shows a barrier with two turning points for energies $E>0$ and below the barrier  height $V_0$.\\

   Fig 2Fig 2. energy $E <0 $ and  unbounded motion for $E>0$.

In the above two examples the turning  points are obtained by solving $V(x)=E$. If the potential is piece wise continuous, this may or may not be the case. For example, for one of the two potentials in Fig. 3 the turning  points are not obtained by solving $E=V(x)$.

                                                                              Figure 3