q-deformed boson oscillators and zero point energy

Just as for the ordinary quantum harmonic oscillators, we expect the zero-p oint energy to play a crucial role in the correct high temperature behavior . We accordingly reformulate the theory of the statistical distribution fun ction for the g-deformed boson oscillators and develop an approximate theor y incorporating the zero-point energy. We are then able to demonstrate that for small deformations, In q much less than 1, the theory reproduces the c orrect limits both for very high temperatures and for very low temperatures . The deformed theory thus reduces to the undeformed theory in these extrem e cases.