Short Examples
A few examples and tips for using WKB formula for bound states are given. qm-xmp-22001
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