state occurs with a small energy and an extended wave function, it opens the gate, and states can move from the right to the left, or vice-versa.

It is possible to study how the spectrum in Fig. \[DW1DaSp\] evolves if the centre of the spike moves to the right, i.e., $R_0\to R_2-R_1$: the dotted line move up and disappear, while the dashed lines move down and become more numerous. Eventually, if the depth $V_1$ is large, the spectrum becomes very similar to the odd part of the spectrum in Figs. \[DW1D\], \[OddEvenSq\], except for a change $R_1\to 2 R_1$ and $R_2\to 2 R_2$.; This illustrates again that for the upper part of the spectrum, a deep hole is equivalent to a hard wall.

Rearrangement in quantum dots
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Level rearrangement in an harmonic well
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There is a considerable recent literature on quantum dots [@0034-4885-64-6-201], usually dealing with many particles in a trap, with a magnetic field. Let us consider the simplified problem of two particles confined by a wide harmonic trap, and interacting with short-range forces, $$\label{eq:dot1}
H={\vec{p}_1^2\over 2m}+{\vec{p}_2^2\over 2 m}+ K r_1^2+Kr_2^2+\lambda v(|\vec{r}_2-\vec{r}_1|)~.$$ The centre-of-mass oscillates in a pure harmonic potential, and the separation $\vec{r}=\vec{r}_2-\vec{r}_1$ is governed by 