Abstract
It is shown that the q-deformed Heisenberg algebra with q being a phase ( q= e iθ , with θ real) can be reduced to Jannussis' Lie-deformed Heisenberg algebra, whose realizations with differential operators are given by Jannussis et al. On the other hand, difference operators satisfying the q-deformed Heisenberg algebra are well-known. In this Letter two different methods are given to show that these two realizations are really identical. On the basis of the above discussions, a possible physical interpretation of q-deformation is given.
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