  In this paper we calculate the basic thermodynamical quantities for a system
of bosonic simple harmonic oscillators (BSHOs) and the corresponding system of
fermionic simple harmonic oscillators (FSHOs) using a dispersion relationship
similar to cases in general relativity and condensed matter physics. In the
FSHO we see negative temperatures in both cases we obtain finally a system of
oscillators with only one effective frequency of vibration. Also we see that
pressure is less than zero for T < Tc where Tc is a critical temperature for
bosons.
