  The current density of states (DOS) calculations do not take into account the
essential discreteness of the state space, since they rely on the unbounded
continuum approximation. Recently, discrete DOS based on the
quantum-mechanically allowable minimum energy interval has been introduced for
quadratic dispersion relation. In this work, we consider systems exhibiting
linear dispersion relation, particularly photons and phonons, and calculate the
related density and number of states (NOS). Also, a Weyl's conjecture-based DOS
function is calculated for photons and phonons by considering the bounded
continuum approach. We show that discrete DOS function reduces to expressions
of bounded and unbounded continua in the appropriate limits. The fluctuations
in discrete DOS completely disappear under accumulation operators. It's
interesting that relative errors of NOS and DOS functions with respect to
discrete ones are exactly the same as the ones for quadratic dispersion
relation. Furthermore, the application of discrete and Weyl DOS for the
calculation of internal energy of a photon gas is presented and importance of
discrete DOS is discussed. It's shown that discrete DOS function given in this
work needs to be used whenever the low energy levels of a physical system are
heavily occupied.
