  In this work, we demonstrate an alternative method of deriving an isotropic
energy band model using a one-dimensional definition of the effective mass and
experimentally observed dependence of mass on energy. We extend the effective
mass definition to anti-particles and particles with zero rest mass. We assume
an often observed linear dependence of mass on energy and derive a generalized
non-parabolic energy-momentum relation. The resulting non-parabolicity leads to
velocity saturation at high particle energies. We apply the energy band model
to free relativistic particles and carriers in solid state materials and obtain
commonly used dispersion relations and experimentally confirmed effective
masses. We apply the model to zero rest mass particles in graphene and propose
using the effective mass for photons. Therefore, it appears that the new energy
band model based on the effective mass can be applied to relativistic particles
and carriers in solid state materials.
