EFFECTIVE DISAPPEARANCE OF DEGENERATING ENERGY-LEVELS

Inverse spectral theory provides a theorem on the shifting of a single level, leaving all others unchanged, in a quantum-mechanical system o ver a finite range in one dimension. We show that the mechanism can be used to remove a pair of states from the spectrum by shifting the ene rgy of one state onto that of a neighboring state. We extend the proce dure to potentials defined on the whole axis possessing a purely discr ete or a partly discrete and partly continuous spectrum.