that for S-states. The study could be pursued for higher value of the orbital momentum and the rearrangement would be observed to become even shaper.

Outlook
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In this article, some remarkable spectral properties of the Schrödinger equation have been exhibited, which occur when a strong short-range interaction is added to a wide attractive well. When the short-range part is deep enough to support one or more bound states, it acts as repulsive barrier on the upper part of the spectrum. Thus the low-lying levels are approximately those which are in wide well, with, however, the condition that the wave function vanishes in the region of strong attraction.

It is interesting to follow the spectrum as a function of the strength of the additional short-range attraction. The energy curve exhibit sharp transitions from intervals where they vary slowly. This is the phenomenon of level-rearrangement, discovered years ago, and generalised here.

It is worth pointing out an important difference between one and higher dimensions regarding rearrangement phenomenon. Since in one dimension, one has the inequality $E_{n-1}<E_n$, there cannot be any crossing of levels during rearrangement. However, while in higher dimensions, there cannot be any crossing between levels with same angular momentum, 