q-oscillators with exotic properties

Abstract:
A class of q-deformed oscillators, containing both previously known ones and some unexplored q-oscillators, is studied with focus on their unusual properties. Concerning such properties, main attention is devoted to the 'accidental' degeneracy (occurring without any underlying symmetry) of energy levels of a wide class of q-oscillators. General statements concerning diverse cases of degeneracies are given and illustrated with a number of particular examples.