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Just as for the ordinary quantum harmonic oscillators, we expect thezero-point energy to play a crucial role in the correct high temperaturebehavior. We accordingly reformulate the theory of the statistical distributionfunction for the q-deformed boson oscillators and develop an approximate theoryincorporating the zero-point energy. We are then able to demonstrate that forsmall deformations, the theory reproduces the correct limits both for very hightemperatures and for very low temperatures. The deformed theory thus reduces tothe undeformed theory in these extreme cases.

q-Deformed Boson Oscillators and Zero Point Energy