$V_1$, is displayed in Fig. \[DW1DaSp\]: Plateaux are observed, again, with energy values corresponding approximately to the combination of $(i)$ the spectrum in a well of depth $-V_2$ between $x=R_0+R_1$ and $x=R_2$ and a hard core on the left, i.e., a boundary condition $w(R_0+R_1)=0$, and $(ii)$ the spectrum in a well of depth $-V_2$ between $x=-R_2$ and $x=R_0-R_1$ with $w(R_0-R_1)=0$.

It is interesting to follow how the wave function evolves when a rearrangement occurs. In Fig. \[DW1DaWf\], the third level is chosen. For $V_1=0$, it is the first even excitation with energy $E_3\simeq -62.18$, and the wave function $u(x)$ is the usual sinus function matching exponential tails. On the first plateau, with energy near $-70$, this wave function is almost entirely located on the right. As rearrangement takes place, the probability is shared by both sides. On the second plateau, with a energy near $-73$ corresponding to the ground state in the wider part with hard wall at $R_0$, the wave function is mostly on the left.

When the narrow well has only deeply bound states, it acts as an effective hard wall between the two boxes, at the right and and the left of $R_0$. However, when a new 