q-Deformed Boson Oscillators and Zero Point Energy

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